# Probability Concise Solutions Chapter-25 ICSE Maths Class-10

## Selina Publishers Maths Chapter-25 Probability

**Probability Concise Solutions Chapter-25** ICSE Maths Class-10.** Solutions** of Exercise – 25 (A), Exercise –25 (B), Exercise – 25 (C) for** Concise **Selina Maths of ICSE Board Class 10th. **Concise **Maths** Solutions Probability **Chapter-25 for ICSE Maths Class 10 is available here. All **Solutions **of **Concise** Selina Maths of **Probability **Chapter-25 has been solved according instruction given by council. This Post is the **Solutions **of **Probability **Chapter-25 for ICSE Class 10th. ICSE **Maths** text book of **Concise** is In series of famous ICSE writer in maths publications. **Concise** is most famous among students

**Probability Concise Solutions Chapter-25 ICSE Maths Class-10**

The **Solutions** of **Concise** Mathematics **Probability **Chapter-25 for ICSE Class 10 have been solved. Experience teachers Solved **Probability **Chapter-25 to help students of class 10th ICSE board. Therefore the ICSE Class 10th Maths **Solutions** of **Concise** Selina Publishers helpful on various topics which are prescribed in most ICSE Maths textbook

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**Exercise – 25 (A) , ****Exercise – 25 (B),**

**How to Solve Concise Maths Selina Publications Chapter-25 ****Probability ****ICSE Maths Class 10**

Note:- Before viewing **Solutions** of Chapter-25 **Probability**** **of **Concise **Selina Maths. Read the Chapter Carefully then solve all example of your text book**. **The Chapter-25 **Probability**** **is main Chapter in ICSE board

**Chapter-25 ****Probability EXERCISE – 25 (A) Concise Solutions ICSE Maths Class-10**

#### Question 1

A coin is tossed once. Find the probability of:

(i) getting a tail

(ii) not getting a tail

#### Answer 1

Sample Space = {H, T}

n(S) = 2

(i) A = Event of getting a tail = {T}

n(A)= 1

Therefore, the probability of getting a tail =

(ii) Not getting a tail

Since P(getting a tail) + P(not getting a tail) = 1

→ P(not getting a tail) = 1 – (1/2) = 1/2

#### Question 2

A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is:

(i) a black ball.

(ii) a red ball.

(iii) a white ball.

(iv) not a red ball.

(v) not a black ball.

#### Answer 2

Total number of balls = 3 + 5 + 2 = 10

Total number of possible outcomes = 10

(i) There are 5 black balls

Number of favourable outcomes = 5

Hence, P(getting a black ball) = 5/10 = 1/2

(ii)

There are 2 red balls

Number of favourable outcomes = 2

Hence, P(getting a red ball) = 2/10 = 1/5

(iii)

There are 3 white balls

Number of favourable outcomes = 3

Hence, P(getting a white ball) = 3/10 = 3/10

(iv)

There are 3 + 5 = 8 balls which are not red

Number of favourable outcomes = 8

Hence, P(getting a white ball) = 8/10 = 4/5

(v)

There are 3 + 2 = 5 balls which are not black

Number of favourable outcomes = 5

Hence, P(getting a white ball) = 5/10 = 1/2

#### Question 3

In a single throw of a die, find the probability of getting a number:

(i) greater than 4.

(ii) less than or equal to 4.

(iii) not greater than 4.

#### Answer 3

Sample space = {1, 2, 3, 4, 5, 6}

n(s) = 6

(i) E = event of getting a number greater than 4 = {5, 6}

n(E)=2

Probability of getting a number not greater than 4 =

#### Question 4

In a single throw of a die, find the probability that the number:

(i) will be an even number.

(ii) will not be an even number.

(iii) will be an odd number.

#### Answer 4

Sample space = {1, 2, 3, 4, 5, 6}

n(s) = 6

(i) E = event of getting an even number = {2, 4, 6}

n(E) = 3

#### Question 5

From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn will:

(i) be a black card.

(ii) not be a red card.

(iii) be a red card.

(iv) be a face card.

(v) and be a face card of red colour.

#### Answer 5

Total number of cards = 52

Total number of outcomes = 52

There are 13 cards of each type. The cards of heart and diamond are red in colour. Spade and diamond are black. So, there are 26 red cards and 26 black cards.

(i) Number of black cards in a deck = 26

The number of favourable outcomes for the event of drawing a black card = 26

Probability of drawing a black card = 26/52 = 1/2

(ii) Number of red cards in a deck = 26

Therefore, number of non-red(black) cards = 52 – 26 = 26

The number of favourable outcomes for the event of not drawing a red card = 26

Probability of not drawing a red card = 26/52 = 1/2

(iii) Number of red cards in a deck = 26

The number of favourable outcomes for the event of drawing a red card = 26

Probability of drawing a red card =26/52= 1/2

(iv) There are 52 cards in a deck of cards, and 12 of these cards are face cards (4 kings, 4 queens, and 4 jacks).

The number of favourable outcomes for the event of drawing a face card = 12

Probability of drawing a face card =12/52= 3/13

(v) There are 26 red cards in a deck, and 6 of these cards are face cards (2 kings, 2 queens, and 2 jacks).

The number of favourable outcomes for the event of drawing a face card of red color = 6

Probability of drawing a red face card =6/52 = 3/26

#### Question 6

(i) If A and B are two complementary events then what is the relation between P(A) and P(B)?

(ii) If the probability of happening an event A is 0.46. What will be the probability of not happening of the event A?

#### Answer 6

(i) Two complementary events, taken together, include all the outcomes for an experiment and the sum of the probabilities of all outcomes is 1.

P(A) + P(B) = 1

(ii) P(A) = 0.46

Let P(B) be the probability of not happening of event A

We know,

P(A) + P(B) = 1

P(B) = 1 – P(A)

and P(B) = 1 – 0.46

P(B) = 0.54

Hence the probability of not happening of event A is 0.54

#### Question 7

In a T.T. match between Geeta and Ritu, the probability of the winning of Ritu is 0.73. Find the probability of:

(i) winning of Geeta

(ii) not winning of Ritu

#### Answer 7

(i) Winning of Geeta is a complementary event to winning of Ritu

Therefore,

P(winning of Ritu) + P(winning of Geeta) = 1

and P(winning of Geeta) = 1 – P(winning of Ritu)

while P(winning of Geeta) = 1 – 0.73

hence P(winning of Geeta) = 0.27

(ii) Not winning of Ritu is a complementary event to winning of Ritu

Therefore,

P(winning of Ritu) + P(not winning of Ritu) = 1

and P(not winning of Ritu) = 1 – P(winning of Ritu)

so P(not winning of Ritu) = 1 – 0.73

hence P(not winning of Ritu) = 0.27

#### Question 8

In a race between Mahesh and John, the probability that John will lose the race is 0.54. Find the probability of:

(i) winning of Mahesh

(ii) winning of John

#### Answer 8

(i) But if John looses, Mahesh wins

Hence, probability of John losing the race = Probability of Mahesh winning the race since it is a race between these two only

Therefore, P(winning of Mahesh) = 0.54

(ii) P(winning of Mahesh) + P(winning of John) = 1

0.54 + P(winning of John) = 1

P(winning of John) = 1 – 0.54

P(winning of John) = 0.46

#### Question 9

(i) Write the probability of a sure event

(ii) Write the probability of an event when impossible

(iii) For an event E, write a relation representing the range of values of P(E)

#### Answer 9

(i) The probability of a sure event is 1 i.e. P(E) = 1 where ‘E’ is the sure event.

Proof: In a sure event n(E) = n(S)

[Since Number of elements in Event ‘E’ will be equal to the number of element in sample-space.]

By definition of Probability :

P(E) = n (E)/ n (S) = 1

P(E) = 1

(ii) The probability of an impossible event is ‘0’ i.e. P (E) = 0

Proof: Since E has no element, n(E) = 0

From definition of Probability:

P(E) = n (E) / n(S) = 0 / n(S)

P(E) = 0

(iii) The probability of an event lies between ‘0’ and ‘1’.

The number of elements in ‘E’ can’t be less than ‘0’ i.e. negative and greater than the number of elements in S.

#### Question 10

In a single throw of die, find the probability of getting:

(i) 5

(ii) 8

(iii) a number less than 8

(iv) a prime number

#### Answer 10

Sample space = {1, 2, 3, 4, 5, 6}

n(S) = 6

(i) E = event of getting a 5 on a throw of die = {5}

n(E) = 1

Probability of getting a 5 =P(E) = n(E)/n(S) = 1/6

(ii) There are only six possible outcomes in a single throw of a die. If we want to find probability of 8 to come up, then in that case number of possible or favourable outcome is 0 (zero)

n(E) = 0

Probability of getting a 8 =P(E) = n(E)/n(S)= 0/6 = 0

(iii) If we consider to find the probability of number less than 8, then all six cases are favourable

n(E) = 6

Probability of getting a number less than 8 =P(E) = n(E)/n(S) = 6/6 = 1

(iv) E = event of getting a prime number = {2, 3, 5}

n(E) = 3

Probability of getting a prime number =P(E) = n(E)/n(S) = 3/6 = 1/2

#### Question 11

A die is thrown once. Find the probability of getting:

(i) an even number

(ii) a number between 3 and 8

(iii) an even number or a multiple of 3

#### Answer 11

Sample space = {1, 2, 3, 4, 5, 6}

n(S) = 6

(i) E = the possible even numbers = {2, 4, 6}

n(E) = 3

Probability of getting an even number =P(E) = n(E)/n(S) = 3/6 =1/2

(ii) E = the possible even numbers between 3 and 8 = {4, 5, 6}

n(E) = 3

Probability of getting an even number between 3 and 8 =P(E) = n(E)/n(S) = 3/6= 1/2

(iii) E = the event of getting an even number or a multiple of 3 = {2, 3, 4, 6}

n(E) = 4

Probability of getting an even number or a multiple of 3 =P(E) = 4/6= 2/3

#### Question 12

Which of the following cannot be the probability of an event?

(i)

(ii) 2.7

(iii) 43%

(iv) -0.6

(v) -3.2

(vi) 0.35

#### Answer 12 Probability Concise Solutions Chapter-25

#### Question 13

A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out:

(i) a white ball

(ii) a black ball

#### Answer 13

Possible number of outcomes = 6 = number of balls in the bag

n(S) = 6

(i) E = event of drawing a white ball = number of white balls in the bag = 0

n(E) = 0

Probability of drawing a white ball =P(E) = n(E)/n(S)= 0/6 =0

(ii) E = event of drawing a black ball = number of black balls in the bag = 6

n(E) = 6

Probability of drawing a black ball =P(E)= n(E)/n(S)=6/6=1

#### Question 14

A single letter is selected at random from the word ‘Probability’. Find the probability that it is a vowel.

#### Answer 14

Possible outcomes = S = {‘P’, ‘r’, ‘o’, ‘b’, ‘a’, ‘b’, ‘i’, ‘l’, ‘i’, ‘t’, ‘y’}

n(S) = 11

Event of selection of vowels = E = {‘o’, ‘a’, ‘i’, ‘i’}

n(E) = 4

Probability of selection of a vowel = P(E)= n(E)/n(S) = 4/11

#### Question 15

Ramesh chooses a date at random in January for a party.

January | |||||

Mon | 6 | 13 | 20 | 27 | |

Tue | 7 | 14 | 21 | 28 | |

Wed | 1 | 8 | 15 | 22 | 29 |

Thurs | 2 | 9 | 16 | 23 | 30 |

Fri | 3 | 10 | 17 | 24 | 31 |

Sat | 4 | 11 | 18 | 25 | |

Sun | 5 | 12 | 19 | 26 |

Find the probability that he chooses:

(i) a Wednesday.

(ii) a Friday.

(iii) a Tuesday or a Saturday.

#### Answer 15

Number of possible outcomes = number of days in the month =31

n(S) = 31

(i) E = event of selection of a Wednesday = {1, 8, 15, 22, 29}

n(E) = 5

Probability of selection of a Wednesday =P(E) = n(E)/n(S)= 5/31

(ii) E = event of selection of a Friday = {3, 10, 17, 24, 31}

n(E) = 5

Probability of selection of a Friday =P(E) = n(E)/n(S)=5/31

(iii) E = event of selection of a Tuesday or a Saturday = {4, 7, 11, 14, 18, 21, 25, 28}

n(E) = 8

Probability of selection of a Tuesday or a Saturday =P(E) = n(E)/n(S)= 8/31

**Concise Maths EXERCISE -25 (B)** **Selina Publications Chapter-25 ****Probability ****ICSE Maths Class 10**

**Question 1.**

**Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be :**

**(i) an even number.**

**(ii) a multiple of 3 ,**

**(iii) an even number and a multiple of 3.**

**(iv) an even number or a multiple of 3.**

#### Answer 1

No. of cards = 9

Having numbers marked on it = 2 to 10

∴ Number of possible outcomes = 9

**(i)** An even number i.e. 2, 4, 6, 8, 10 = 5

∴ Number of even numbers = 5

**Question 2.**

**Hundred identical cards are numbered from 1 to 100. The cards are well shuffled and then a card is drawn. Find the probability that the number on the card drawn is :**

**(i) a multiple of 5.**

**(ii) a multiple of 6.**

**(iii) between 40 and 60.**

**(iv) greater than 85.**

**(v) less than 48.**

#### Answer 2

Number of cards = 100

Marked with numbers from 1 to 100

∴ Number of possible outcome = 100

**(i)** A multiple of 5 are 5, 10, 15 95, 100

which are 20 in numbers.

∴ Number of favourable outcome = 20

**Question 3.**

**From 25 identical cards, numbered, 1, 2, 3, 4, 5 ,…………, 24, 25 ; one card is drawn at random.**

**Find the probability that the number on the card drawn is a multiple of :**

**(i) 3 (ii) 5 (iii) 3 and 5 (iv) 3 or 5**

#### Answer 3

Number of identical cards = 25

Numbers marked on their are 1 to 25 i.e.

1, 2, 3, 4, 5, …. 21, 22, 23, 24, 25

∴ Number of possible outcome = 25

**(i)** Multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24

Which are 8 in numbers.

**Question 4. Probability Concise Solutions Chapter-25**

**A die is thrown once. Find the probability of getting a number :**

**(i) less than 3.**

**(ii) greater than or equal to 4.**

**(iii) less than 8**

**(iv) greater than 6.**

#### Answer 4

A die has 6 numbers i.e., 1, 2, 3, 4, 5, 6

∴ Number of possible outcome = 6

**(i)** Less than 3 are 1, 2 which are 2 in numbers

**Question 5.**

**A book contains 85 pages. A page is chosen at random. What is the probability that the sum of the digits on the page is 8 ?**

#### Answer 5

Number of pages of the book = 85

which are from 1 to 85

Number of possible outcome = 85

∴ Number of pages whose sum of its page is 8 are : 17, 26, 35, 44, 53, 62, 71, 80 and 8

**Question 6.**

**A pair of dice is thrown. Find the probability of getting a sum of 10 or more if 5 appears on the first die.**

Answer 6

Numbers marked on each die = 6

∴ Total number of cases = 6 x 6 = 36

∵ Favourable come are (5, 5), (5, 6) as 5 appears on the first, which are 2 in number

**Question 7.**

**If two coins are tossed once, what is the probability of getting :**

**(i) 2 heads**

**(ii) at least one head**

**(iii) both heads or both tails.**

#### Answer 7

∵ A coins has two faces Head and Jail or H, T

∴ Two coins are tossed

∴ Number of coins = 2 x 2 = 4

which are HH, HT, TH, TT

**(i)** When both are Head, then

∴ Number of outcome = 1

**Question 8. Probability Concise Solutions Chapter-25**

**Two dice are rolled together. Find the probability of getting :**

**(i) a total of at least 10.**

**(ii) a multiple of 2 on one die and an odd number on the other die.**

#### Answer 8

∵ A die has 6 faces which are 1, 2, 3, 4, 5,6

∴ On rolling two dice at a time, number of comes = 6 x 6 = 36

∴ Number of possible outcome = 36

**(i)** a total of atleast 10, the favourable can be (4,6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6) which are 6 in number

**Question 9.**

**A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is :**

**(i) a spade.**

**(ii) a red card.**

**(iii) a face card.**

**(iv) 5 of heart or diamond.**

**(v) Jack or queen.**

**(vi) ace and king.**

**(vii) a red and a king.**

**(viii) a red or a king.**

#### Answer 9

A pack of playing card has 52 cards

∴ Number of possible outcome = 52

**(i)** A spade

∵ there are 13 cards of spade

∴ Number of favourable outcome = 13

**Question 10. Probability Concise Solutions Chapter-25**

**A bag contains 16 coloured balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is :**

**(i) red**

**(ii) not red**

**(iii) white**

**(iv) not white**

**(v) green or red**

**(vi) white or green**

**(vii) green or red or white.**

#### Answer 10

Number of balls in a bag = 16

Green balls = 6

White balls = 3

Red balls = 7

∴ Total possible outcome =16

**(i)** Red balls = 7

**Question 11.**

**A ball is drawn at random from a box .ontammg 12 white. 16 red and 20 green balls. Determine the probability that the ball drawn is:**

**(i) white**

**(ii) red**

**(iii) not green**

**(iv) red or white**.

#### Answer 11

Number of balls in a box

White = 12

Red = 16

Green = 20

Total balls = 12 + 16 +20 = 48

∴ Total possible outcome = 48

**(i)** White balls = 12

∴ Number of favourable outcome =12

**Question 12.**

**A card is drawn from a pack of 52 cards. Find the probability that the card drawn is :**

**(i) a red card**

**(ii) a black card**

**(iii) a spade**

**(iv) an ace**

**(v) a black ace**

**(vi) ace of diamonds**

**(vii) not a club**

**(viii) a queen or a jack**

#### Answer 12

Number of cards in playing card deck = 52

∴ Number of possible outcome = 52

**(i)** A red card

There are 13 + 13 = 26 red cards in the deck

∴ Number of favourable outcome = 26

**Question 13. Probability Concise Solutions Chapter-25**

**Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is :**

**(i) a multiple of 4 or 6.**

**(ii) a multiple of 3 and 5**

**(iii) a multiple of 3 or 5**

#### Answer 13

There are 30 cards which are marks with numbers 1 to 30 and one card is drawn

**(i)** A multiple of 4 or 6.

∴ There are multiple of 4 or 6 = 4,6, 8, 12, 16, 18, 20, 24, 28, 30 which are 10

**Question 14.**

**In a single throw of two dice, find the probability of :**

**(i) a doublet**

**(ii) a number less than 3 on each dice.**

**(iii) an odd number as a sum.**

**(iv) a total of at most 10.**

**(v) an odd number on one dice and a number less than or equal to 4 on the other dice.**

#### Answer 14

Number of dice thrown = 2

Each die has 1 to 6 numbers on its faces Number of possible outcomes = 6 X 6 = 36

**(i)** A doublet : These can be (1, 1), (2, 2),(3, 3), (4, 4), (5, 5) and (6, 6) which are 6

∴ Number of favourable outcome = 6

### Solutions of Concise Selina ICSE Maths Chapter-25 Probability **EXERCISE – 25(C)**

**Question 1.**

**A bag contains 3 red balls, 4 blue balls and one yellow ball, all the balls being identical in shape and size. If a ball is taken out of the bag without looking into it : find the probability that die ball is :**

**(i) yellow**

**(ii) red**

**(iii) not yellow**

**(iv) neither,yellow nor red**

#### Answer 1

In a bag. there are 8 balls in which there are Red balls = 3

blue balls = 4

and yellow ball = 1

Total possible out come = 8

**(i)** Yellow balls = 1

∴ Number of favourable outcome = 1

**Question 2.**

**A dice is thrown once. What is the probability of getting a number :**

**(i) greater than 2 ?**

**(iii) less than or equal to 2 ?**

#### Answer 2

A die is thrown once

Numbers marked on the faces of a die are 1, 2,3,4, 5, 6

∴ Number of possible outcome = 6

**(i)** Greater than 2 number = 3, 4, 5, 6 = 4 numbers

**Question 3. Probability Concise Solutions Chapter-25**

**From a well-shuffled deck of 52 cards* one card is drawn. Find the probability that the card drawn is :**

**(i) a face card.**

**(ii) not a face card. ,**

**(iii) a queen of black colour.**

**(iv) a card with number 5 or 6.**

**(v) a card with number less than 8.**

**(vi) a card with number between 2 and 9.**

#### Answer 3

A deck of playing cards has 52 cards

∴ Number of possible outcome = 52

**(i)** A face card ; face cards in the deck are = 3 x 4 = 12

∴ Number of favourable outcome = 12

**Question 4.**

**In a match between A and B.**

**(i) the probability of winning of A is 0.83. What is the probability of winning of B ?**

**(ii) the probability of losing the match is 0.49 for**

**B. What is the probability of winning of A?**

#### Answer 4

A match is played between two persons A and B

∴ Number of possible outcome = 1

**(i)** The probability of winning of A is 0.83

∴ Probability of winning of B = 1 – 0.83 = 0.17 [∵ P(E) + P( )=1]

**(ii)** The probability of losing the match is 0.49 by B.

∴ Probability of losing of B or winning of A = 0.49

**Question 5.**

**A and B are friends. Ignoring the leap year, find the probability that both friends will have :**

**(i) different birthdays ?**

**(ii) the same birthdays ? (Ignore a leap year)**

#### Answer 5

Number of days in a year = 365

and birthday of a person can be on one day only.

**(i)** Different birthdays can be 365 – 1 = 364

**Question 6.**

**A man tosses two different coins (one of Rs. 2 and another of Rs. 5) simultaneously. What is the probability that he gets :**

**(i) at least one head ?**

**(ii) at most one head?**

#### Answer 6

There are two coins : one of two rupees and

other is of 5-rupees

∴ Number of Heads =1 + 1=2

and number of tails are 2 i.e., 2 and 5

∴ Number of possible outcome = 2 x 2 = 4

**(i)** Atleast one head.

Number of favourable outcome = 3

**Question 7.**

**A box contains 7 red balls, 8 green balls and 5 white balls. A ball is drawn at random from the box. Find the probability that the ball is :**

**(i) white**

**(ii) neither red nor white**

#### Answer 7 Probability Concise Solutions Chapter-25

Number of balls in a box are 20 in which 7 are red, 8 are green and 5 are white

∴ Number of possible outcome = 20

**(i)** White = 5

∴ Number of favourable outcome = 5

**Question 8.**

**All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting :**

**(i) a black face card**

**(ii) a queen**

**(iii) a black card.**

#### Answer 8

A deck of playing cards = 52

Cards which are removed = 3 (3 face cards of spades)

Balance cards in the deck = 52 – 3 = 49

**(i)** A black face card which are 6 – 3 = 3 in number

∴ Number of favourable outcome = 3

**Question 9.**

**In a musical chairs game, a person has been advised to stop playing the music at any time within 40 seconds after its start.**

**What is the probability that the music will stop within the first 15 seconds ?**

#### Answer 9

Total time for the musical race = 0 to 40 seconds = 40 seconds.

Time taken by a player =15 seconds. (0 to 15 seconds)

**Question 10.**

**In a bundle of 50 shirts, 44 are good, 4 have minor defects and 2 have major defects. What is the probability that :**

**(i) it is acceptable to a trader who accepts only a good shirt ?**

**(ii) it is acceptable to a trader who rejects only a shirt with major defects ?**

#### Answer 10

Total number of shirts in a bundle = 50

No. of good shirts = 44

Minor defected = 4

Major defected = 2

∴ Number of possible outcome = 50

**(i)** Acceptance of only for a good shirt = 44

**Question 11.**

**Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is :**

**(i) 8**

**(ii) 13**

**(iii) less than or equal to 12**

#### Answer 11

Two dice are thrown at the same time and each dice has 6 numbers 1, 2, 3, 4, 5, 6 on its faces

∴Number of possible outcome = 6 x 6 = 36

**(i)** Sum of two numbers on the top is 8 i.e..(2, 6), (3, 5), (4,4), (5, 3), (6, 2)

∴ Number of favourable outcome = 5

**Question 12.**

**Which of the following cannot be the probability of an event ?**

**(i) **

**(ii) 0.82**

**(iii) 37%**

**(iv) -2.4**

#### Answer 12

**(i)** ∵ is between 0 and 1

∴ It is a probability event

**(ii)** ∵ 0.82 is between 0 and 1

∴ It is a probability event.

**(iii)** 37% =

∵It is between 0 and 1

∴ It is a probability event.

**(iv)** -2.4

∵It is less than 0.

∴ It is not a probability event.

**Question 13.**

**If P(E) = 0.59; find P(not E).**

#### Answer 13

P(E) = 0.59

But P(E) + P( )= 1

or P(E) + P(not E) = 1

⇒ 0.59 + P(not E) = 1

⇒ ∴ P(not E) = 1 – 0.59 = 0.41

**Question 14. Probability Concise Solutions Chapter-25**

**A bag contains a certain number of red balls. A ball is drawn. Find the probability that the ball drawn is :**

**(i) black**

**(ii) red.**

#### Answer 14

In a bag, there are certain number red balls. Let it be x balls.

One ball is drawn out

**(i)** A black

∵ There is no black ball in the bag

∴ Probability of black ball = 0

**(ii)** A red ball

**Question 15.**

**The probability that two boys do not have the same birthday is 0.897. What is the probability that the two boys have the same birthday ?**

#### Answer 15

Probability of two boys do not have the same birthday [P (E)] = 0.897

Let Probability of those boys having the same birthday = P(not E)

= P( )

But P(E) + P( )= 1

⇒ 0.897 +P( ) = 1

⇒P( )= 1 -0.897 = 0.103

Hence probability having the same birthday = 0.103

**Question 16.**

**A bag contains 10 red balls, 16 white balls and 8 green balls. A ball is drawn out of the bag at random. What is the probability tharthe ball drawn will be :**

**(i) not red ?**

**(ii) neither red nor green ?**

**(iii) white or green ?**

#### Answer 16

In a bag, there are 10 red balls, 16 white and 8 green balls

∴ Total balls =10 + 16 + 8= 34 ball

∴ Number of possible outcome = 34

**(i)** Not red ball

Number of favourable outcome = 16 + 8 = 24

**Question 17.**

**A bag contains twenty Rs. 5 coins, fifty Rs. 2 coins and thirty Re 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin :**

**(i) will be a Re 1 coin ?**

**(ii) will not be a Rs. 2 coin ?**

**(iii) will neither be a Rs. 5 coin nor be a Re 1 coin ?**

#### Answer 17

In a bag, there are

5-rupee coins = 20

2-rupee coins = 50

1-rupee coin =30

Total number of coins in the bag = 20 + 50 + 30 = 100

∴ Number of possible outcome =100

**(i)** one-rupee coin = 30

**Question 18.**

**A game consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; as shown below.**

**If the outcomes are equally likely, find the probability that the pointer will point at :**

**(i) 6**

**(ii) an eve., number.**

**(iii) a prime number.**

**(iv) a number greater than 8.**

**(v) a number less than or equal to 9.**

**(vi) a number between 3 and 11.**

#### Answer 18

There are 12 numbers on the spinning game.

∴ Number of possible outcome = 12

**Question 19. Probability Concise Solutions Chapter-25**

**One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting :**

**(i) a queen of red colour.**

**(ii) a black face card.**

**(iii) the jack or the queen of hearts.**

**(iv) a diamond.**

**(v) a diamond or a spade.**

#### Answer 19

Number of cards in a deck of playing card = 52

∴ Number of possible outcome = 52

**(i)** A queen of red colour

Number of favourable outcome = 2

(As there are 2 red queens in the deck)

**Question 20.**

**From a deck of 52 cards, all the face cards are removed and then the remaining cards are shuffled. Now one card is drawn from the remaining deck. Find the probability that the card drawn is :**

**(i) a black card.**

**(ii) 8 of red color.**

**(iii) a king of black color.**

#### Answer 20

Number of cards is a deck of playing card = 52

All face cards are removed. Which are 3 x 4 = 12

**(i)** A black card which are 10 in numbers

**Question 21. Probability Concise Solutions Chapter-25**

**Seven cards : – the eight, the nine, the ten, jack, queen, king and ace of diamonds are well shuffled. One card is then picked up at random.**

**(i) What is the probability that the card drawn is the eight or the king ?**

**(ii) If the king is drawn and put aside, what is the probability that the second card picked up is**

**(a) an ace ?**

**(b) a king ?**

#### Answer 21

There are 7 cards which are the eight, the nine, the ten, the jack, the’ queen, the king and the ace of diamond.

∴ Number of possible outcome = 7

**(i)** card having the eight or a king which are 2.

**Question 22.**

**A box contains 150 bulbs out of which 15 are defective. It is not possible to just look at a bulb and tell whether or not it is defective. One bulb is taken out at random from this box. Calculate the probability that the bulb taken out is :**

**(i) a good one**

**(ii) a defective one.**

#### Answer 22

Number of bulbs in a box = 150

No. of defective bulbs = 15

∴ No of good bulbs = 150 – 15 = 135

∴ Number of possible outcome = 150

**(i)** A good bulb and number of good bulbs =135

**Question 23.**

**(i) 4 defective pens are accidentally mixed with 16 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is drawn at random from the lot. What is the probability that the pen is defective ? (ii) Suppose the pen drawn in (i) is defective and is not replaced. Now one more pen is drawn at random from the rest. What is the probability that this pen is :**

**(a) defective**

**(b) not defective ?**

#### Answer 23

Number of defective pens = 4

**(i)** and number of good pens = 16

∴ Total pens = 4 + 16 = 20

∴ Number of possible outcome = 20

One defective pen, no. of defective pens = 4

**Question 24.**

**A bag contains 100 identical marble stones which are numbered from 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears :**

**(i) a perfect square number.**

**(ii) a number divisible by 4.**

**(iii) a number divisible by 5.**

**(iv) a number divisible by 4 or 5.**

**(v) a number divisible by 4 and 5.**

#### Answer 24

Total number of stones = 100

On which numbers 1 to 100 are marked

∴ Number of possible outcome = 100

**(i)** A perfect square = which are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 which are 10 inmumbers

**Question 25.**

**A circle with diameter 20 cm is drawn somewhere on a rectangular piece of paper with length 40 cm and width 30 cm. This paper is kept horizontal on table top and a die, very small in size, is dropped on the rectangular paper without seeing towards it. If the die falls and lands on the paper only, find the probability that it will fall and land :**

**(i) inside the circle.**

**(ii) outside the circle.**

#### Answer 25

Diameter of the circle = 20 cm

Length of rectangular paper = 40 cm

and width = 30 cm

Area of rectangle = 40 x 30 = 1200 cm2

∴ Number of possible out come = 1200

**Question 26.**

**Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is :**

**(i) 4 or 5**

**(ii) 7, 8 or 9.**

**(iii) between 5 and 8**

**(iv) more than 10**

**(v) less than 6**

#### Answer 26

Two dice having numbers 1 to 6 are rolled together.

∴ Number of possible outcome = 6 x 6 = 36

**(i)** If sum is 4 or 5 of numbers on the upper most face,

Their number of favourable outcome = (1,3), (2, 2), (3, 1), (1, 4), (2, 3), (3, 2), (4, 1) which are 7 in numbers

**Question 27. Probability Concise Solutions Chapter-25**

**Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting :**

**(i) exactly two heads.**

**(ii) at least two heads.**

**(iii) atmost two heads.**

**(iv) all tails.**

**(v) at least one tail.**

#### Answer 27

3 coins one tossed together.

∴ Number of possible outcome = 23 = 2 x 2 x 2 = 8

i.e. HHH, HHT, HTH, HTT, TTT, THH, THT, TTH

**(i)** exactly two heads these can be HHT, THH, HTH = 3 in numbers

**Question 28.**

**Two dice are thrown simultaneously. What is the probability that :**

**(i) 4 will not come up either time ?**

**(ii) 4 will come up at least once ? **

#### Answer 28

Two dice are thrown simultaneous,

and each dice has 1-6 numbers on its faces

∴ Number of possible outcome = 6 x 6 = 36

**(i)** 4 will not come up either time

∴ Number of favourable outcomes = (6 – 1)² = (5)² = 25

**Question 29.**

**Cards marked with numbers 1, 2, 3, 4, …,20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is**

**(i) a prime number**

**(ii) divisible by 3**

**(iii) a perfect square ?**

#### Answer 29

**Question 30.**

**Offices in Delhi are open for five days in a week (Monday to Friday). Two employees of an office remain absent for one day in the same particular week. Find the probability that they remain absent on :**

**(i) the same day**

**(ii) consecutive day**

**(iii) different days.**

#### Answer 30

∵ Office are open for 5 days a week

∴ Number of possible outcomes for 2 employees = 5 x 5 = 25

Let the five days of working be denoted by M, T, W, Th, F for Mondays, Tuesday, Wednesday Thursday and Friday respectively

**(i)** On Same day.

Favourable outcome will be M;T;T;M;T;W;W;T;W;H; TH.W ; TH ; F and F, TH which are 8 in all

**Question 31. Probability Concise Solutions Chapter-25**

**A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of white ball; find the number of black balls in the box.**

#### Answer 31

In a box, some balls are black while 30 balls are white

Let number of black balls = x

Then number of possible outcome = x + 30

Probability of drawing a black ball = of a white balls.

Now, In case of black ball,

**Question 32.**

**From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn at random.**

**What is the probability that the card drawn is**

**(i) a face card (King, Jack or Queen)**

**(ii) an even numbered red card ? (2011)**

#### Answer 32

No. of total cards = 52 cards removed of 4 colors = 3, 6, 9, 12 = 4 x 4 = 16

Remain using cards = 52 – 16 = 36

**(i)** No. of faces cards = 2 x 4 = 8 cards (excluding queen)

∴ Probebility P(E) = =

**(ii)** An even number red cards = 2, 4, 8, 10 = 4×2 = 8 cards

∴ Probebility P(E) = =

**Question 33.**

**A die has 6 faces marked by the given numbers as shown below:**

**The die is thrown once. What is the probability of getting**

**(i) a positive integer.**

**(ii) an integer greater than -3.**

**(iii) the smallest integer.**

#### Answer 33

Total outcomes n(S)= 6

(i) a positive integer = (1, 2, 3)

No. of favourables n(E) = 3

**Question 34.**

**A bag contains 5 white balls, 6 red balls and 9 green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is :**

**(i) a green ball.**

**(ii) a white or a red ball.**

**(iii) neither a green ball nor a white ball. (2015)**

#### Answer 34

A bag contains 5 white balls, 6 red balls and 9 green balls.

∴ Total number of balls = 5 + 6 + 9 = 20 balls

One ball is drawn at random.

**(i)** Probability of a green ball =

**(ii)** Probability of a white or a red ball = =

**(iii)** Probability of neither a green ball nor a white ball = = (Only red balls )

**Question 35. Probability Concise Solutions Chapter-25**

**A game of numbers has cards marked with 11, 12, 13, , 40. A card is drawn at random. Find the probability that the number on the card drawn is :**

**(i) A perfect square**

**(ii) Divisible by 7**

#### Answer 35

**(i)** The perfect squares lying between 11 and 40 and 16, 25 and 36.

So the number of possible outcomes is 3.

Total number of cards from 11 to 40 is 40 – 11 + 1 = 30

Probability that the number on the card drawn is a perfect square

#### Question 36

Sixteen cards are labelled as a, b, c, … , m, n, o, p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is:

- i. a vowel
- a consonant

iii. none of the letters of the word median?

#### Answer 36

Here, Total number of all possible outcomes = 16

- i. a, e,iand o are the vowels.

Number of favourable outcomes = 4

Question 37

A box contains a certain number of balls. On each of 60% balls, letter A is marked. On each of 30% balls, letter B is marked and on each of remaining balls, letter C is marked. A ball is drawn from the box at random. Find the probability that the ball drawn is:

- i. marked C
- A or B

iii. neither B nor C

#### Answer 37

A box contains,

60% balls, letter A is marked.

30% balls, letter B is marked.

10% balls, letter C is marked.

- i. Total number of all possible outcomes = 100

Number of favourable outcomes = 10

Question 38

A box contains a certain number of balls. Some of these balls are marked A, some are marked B and the remaining are marked C. When a ball is drawn at random from the box P(A) = and P(B) =. If there are 40 balls in the box which are marked C, find the number of balls in the box.

#### Answer 38

**–: End of Chapter-25 Probability Concise Maths Solutions :–**

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