ML Aggarwal Probability Exe-22 Class 10 ICSE Maths Solutions Ch-22. We Provide Step by Step Answer of Exe-22 Questions for Ch-22 Matrices as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-10.

## ML Aggarwal Probability Exe-22 Class 10 ICSE Maths Solutions Ch-22

Board | ICSE |

Subject | Maths |

Class | 10th |

Chapter-22 | Probability |

Writer / Book | Understanding |

Topics | Solutions of Exe-22 |

Academic Session | 2024-2025 |

**Probability Exe-22**

ML Aggarwal Class 10 ICSE Maths Solutions Ch-22

**Question 1. ****A box contains 600 screws, one-tenth are rusted. One screw is taken out at random from this box. Find the probability that it is a good screw.**

**Answer :**

Number of total screws = 600

Rusted screws = of 600 = 60

∴ Good screws = 600 – 60 = 540

Probability of a good screw

P(E) = number of favorable outcome/number of possible outcome

= 540/600

= 9/10

**Question 2. ****In a lottery, there are 5 prized tickets and 995 blank tickets. A person buys a lottery ticket. Find the probability of his winning a prize.**

**Answer :**

Number of prized tickets = 5

Number of blank tickets = 995

Total number of tickets = 5 + 995 = 1000

Probability of prized ticket

P(E) = number of favourable outcome/number of possible outcome

= 5/1000

= 1/200

**Question 3. ****12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.**

**Answer :**

Number of defective pens = 12

Number of good pens = 132

Total number of pens =12 + 132 = 144

Probability of good pen

P(E) = number of favourable outcome/number of possible outcome

= 132/144

= 11/12

**Question 4. ****Two players, Sania and Sonali play a tennis match. It is known that the probability of Sania winning the match is 0.69. What is the probability of Sonali winning ?**

**Answer :**

Probability of Sania’s winning the game = 0.69

Let P (E) be the probability of Sania’s winning the game

and P () be the probability of Sania’s losing

the game or probability of Sonali, winning the game

P (E) + P () = 1

⇒ 0.69 + P () = 1

⇒ P() = 1 – 0.69 = 0.31

Hence probability of Sonali’s winning the game = 0.31

**Question 5. ****A bag contains 3 red balls and 5 black balls. A ball is drawn at random’ from in bag. What is the probability that the ball drawn is .**

**(i) red ?**

**(ii) not red ?**

**Answer :**

Number of red balls = 3

Number of black balls = 5

Total balls = 3 + 5 = 8

Let P (E) be the probability of red balls,

then P () will be the probability of not red balls.

P (E) + P () = 1

(i) But P(E) = number of favourable outcome/number of possible outcome

= 3\8

(ii) = 1 – P(E)

= 1-6/11

=( 8-3)/8

= 5/8

**Question 6. ****A letter is chosen from the word ‘TRIANGLE’. What is the probability that it is a vowel ?**

**Answer 6**

There are three vowels: I, A, E

.’. The number of letters in the word ‘TRIANGLE’ = 8.

Probability of vowel

P(E) = number of favourable outcome/number of possible outcome

= 3/8

**Question 7. ****A letter of English alphabet is chosen at random. Determine the probability that the letter is a consonant.**

**Answer :**

No. of English alphabet = 26

and No. of vowel = 5

while No. of constant = 25 – 5 = 21

P(E) = number of favourable outcome/number of possible outcome

= 21/26

**Question 8. ****A box contains 7 blue, 8 white and 5 black marbles. If a marble is drawn at random from the box, what is the probability that it will be**

**(i) black?**

**(ii) blue or black?**

**(iii) not black?**

**(iv) green****?**

**Answer :**

Total number of marbles in the box

= 7 + 8 + 5 = 20

Since, a marble is drawn at random from the box

##### (i) Probability (of a black Marble)

P(E) = number of favourable outcome/number of possible outcome

= 5/20

= 1/4

##### (ii) Probability (of a blue or black marble)

P(E) =number of favourable outcome/number of possible outcome

=( 7+5)/20

and = 12/20

hence = 3/5

##### (iii) Probability (of not black marble)

= 1 – P (of black 1)

and = 1-1/4

so =( 4-1)/4

Hence = 3/4

(iv) P (of a green marble) = 0

(∴ Since, a box does not contain a green marble,

so the probability of green marble will be zero)

**Question 9. ****A bag contains 6 red balls, 8 white balls, 5 green balls and 3 black balls. One ball is drawn at random from the bag. Find the probability that the ball is :**

**(i) white**

**(ii) red or black**

**(iii) not green**

**(iv) neither white nor black.**

**Answer :**

In a bag,

Number of red balls = 6

and Number of white balls = 8

while Number of green balls = 5

and number of black balls = 3

Total number of balls in the bag

= 6 + 8 + 5 + 3 = 22

**(i) Probability of white balls**

P(E) = number of favourable outcome/number of possible outcome

= 8/22

= 4/11

**(ii) Probability of red or black balls**

P(E) = number of favourable outcome/number of possible outcome

=( 6+3)/22

= 9/22

**(iii) Probability of not green balls i.e. having red, white and black balls.**

P(E) = number of favourable outcome/number of possible outcome

= (6+8+3)/22

= 17/22

**(iv) Probability of neither white nor black balls i.e. red and green balls**

P(E) = number of favourable outcome/number of possible outcome

= (6+5)/22

= 11/22

= 1/2

**Probability Exe-22**

ML Aggarwal Probability MCQs Class 10 ICSE Maths Solutions Ch-22

**Page 541**

**Question 10. ****A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Peter, a trader, will only accept the shirts which are good, but Salim, another trader, will only reject the shirts which have major defects. One shirts is drawn at random from the carton. What is the probability that:**

**(i) it is acceptable to Peter ?**

**(ii) it is acceptable to Salim ?**

**Answer :**

In a carton, there the 100 shirts.

Among these number of shirts which are good = 88

number of shirts which have minor defect = 8

number of shirt which have major defect = 4

Total number of shirts = 88 + 8 + 4 = 100

Peter accepts only good shirts i.e. 88

Salim rejects only shirts which have major defect i.e. 4

**(i) Probability of good shirts which are acceptable to Peter**

P(E) = number of favourable outcome/number of possible outcome

= 88/100

= 22/25

**(ii) Probability of shirts acceptable to Salim**

P(E) = number of favourable outcome/number of possible outcome

= (88+8)/100

= 96/100

= 24/25

**Question 11. ****A die is thrown once. What is the probability that the**

**(i) number is even**

**(ii) number is greater than 2 ? (2009)**

**Answer :**

Dice is thrown once

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

**(i) No. of ways in favour = 3**

(∵ Even numbers are 2, 4, 6)

Total ways = 6

Probability = =

**(ii) No. of ways in favour = 4**

(Numbers greater than 2 are 3, 4, 5, 6)

Total ways = 6

Probability = 4/6 = 2\2

**Question 12. ****In a single throw of a die, find the probability of getting:**

**(i) an odd number**

**(ii) a number less than 5**

**(iii) a number greater than 5**

**(iv) a prime number**

**(v) a number less than 8**

**(vi) a number divisible by 3**

**(vii) a number between 3 and 6**

**(viii) a number divisible by 2 or 3.**

**Answer :**

A die is thrown and on its faces, numbers 1 to 6 are written.

Total numbers of possible outcomes = 6

**(i) Probability of an odd number,**

odd number are 1, 3 and 5

P(E) = number of favourable outcome/number of possible outcome

= 3/6

= 1/2

**(ii) A number less them 5 are 1, 2, 3, 4**

Probability of a number less than 5 is

P(E) = number of favourable outcome/number of possible outcome

= 4/6

= 2/3

**(iii) A number greater than 5 is 6**

Probability of a number greater than 5 is

P(E) = number of favourable outcome/number of possible outcome

= 1/6

**(iv) Prime number is 2, 3, 5**

Probability of a prime number is

P(E) = number of favourable outcome/number of possible outcome

= 3/6

= 1/2

**(v) Number less than 8 is nil**

P (E) = 0

**(vi) A number divisible by 3 is 3, 6**

Probability of a number divisible by 3 is

P(E) = number of favourable outcome/number of possible outcome

= 2/6

= 1/3

**(vii) Numbers between 3 and 6 is 4, 5**

Probability of a number between 3 and 6 is

P(E) = number of favourable outcome/number of possible outcome

= 2/6

= 1/3

**(viii) Numbers divisible by 2 or 3 are 2, 4 or 3,**

Probability of a number between 2 or 3 is

P(E) = number of favourable outcome/number of possible outcome

= 2/6

= 1/3

**Question 13. ****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 :**

Total outcomes n(S)= 6

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

No. of favourables n(E) = 3

Probability = n(E)/n(S)

= 3/6

= 1/2

**(ii) Integer greater than -3**

= (1, 2, 3, -1, -2)

No. of favourables n(E) = 5

Probability = n(E)/n(S)

= 5/6

**(iii) Smallest integer = -3**

No. of favourables n(E) = 1

Probability = n(E)/n(S)

= 1/6

**Question 14. ****A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (shown in the adjoining figure) and these are equally likely outcomes. What is the probability that it will point at**

**(i) 8 ?**

**(ii) an odd number ?**

**(iii) a number greater than 2?**

**(iv) a number less than 9?**

**Answer :**

On the face of a game, numbers 1 to 8 is shown.

Possible outcomes = 8

**(i) Probability of number 8 will be**

P(E) = number of favourable outcome/number of possible outcome

= 1/8

**(ii) Odd number are 1, 3, 5, 7**

Probability of a number which is an odd will be

P(E) = number of favourable outcome/number of possible outcome

= 4/8

= 1/2

**(iii) A number greater than 2 are 3, 4, 5, 6, 7, 8 which are 6**

Probability of number greater than 2 will be

P(E) = number of favourable outcome/number of possible outcome

= 6/8

= 3/4

**(iv) A number less than 9 is 8.**

Probability of a number less than 9 will be

P(E) = number of favourable outcome/number of possible outcome

= 8/8

**Question 15. ****Find the probability that the month of January may have 5 Mondays in**

**(i) a leap year**

**(ii) a non-leap year.**

**Answer :**

In January, there are 31 days and in an ordinary year,

there are 365 days but in a leap year, there are 366 days.

**(i) In January of an ordinary year, there are 31 days i.e. 4 weeks and 3 days.**

Probability of Monday will be = 3/7

**(ii) In January of a leap year, there are 31 days i.e. 4 weeks and 3 days**

Probability of Monday will be = 3\7

**Question 16. ****Find the probability that the month of February may have 5 Wednesdays in**

**(i) a leap year**

**(ii) a non-leap year.**

**Answer :**

In the month of February, there are 29 days in a leap year

while 28 days in a non-leap year,

(i) In a leap year, there are 4 complete weeks and 1 day

Probability of Wednesday = P (E) = 1\7

(ii) and in a non leap year, there are 4 complete weeks and 0 days

Probability of Wednesday P (E) = 0/7 = 0

**Question 17. ****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**

**(ii) a consonant**

**(iii) none of the letters of the word median.**

**Answer :**

Here, sample space (S) = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p)

∴n(S) = 16

**(i) Vowels (V) = {a, e, i, o}**

∴n(V) = 4

∴P(a vowel) = n(V)/n(S) = 4/16 = 1/4

**(ii) Consonants (C) = {b, c, d, f, g, h, j, k, l, m, n, p}**

∴n(C) = 12

∴P (a consonant) =n(C)/n(S) = 12/16 = 3/4

**(iii) None of the letters of the word MEDIAN (N) = {b, c, f, g, h, j, k, l, o, p)**

∴n(N) = 10

∴P (N) = n(N)/n(S) = 10/16 = 5/8

**Question 18. ****An integer is chosen between 0 and 100. What is the probability that it is**

**(i) divisible by 7?**

**(ii) not divisible by 7?**

**Answer :**

Integers between 0 and 100 = 99

(i) Number divisible by 7 are

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98 = 14

Probability = 14\99

(ii) Not divisible by 7 are 99 – 14 = 85

Probability = 85/99

**Question 19. ****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 ? (2010)**

**Answer :**

Number cards is drawn from 1 to 20 = 20

One card is drawn at random

No. of total (possible) events = 20

**(i) The card has a prime number**

The prime number from 1 to 20 are 2, 3, 5, 7, 11, 13, 17, 19

Actual No. of events = 8

P(E) = number of favourable outcome/number of possible outcome

= 8/20

= 2/5

**(ii) Numbers divisible by 3 are 3, 6, 9, 12, 15, 18**

No. of actual events = 6

P(E) = number of favourable outcome/number of possible outcome

= 6/20

= 3/10

**(iii) Numbers which are perfect squares = 1, 4, 9, 16 = 4**

P(E) = number of favourable outcome/number of possible outcome

= 4/20

= 1/5

**Question 20. **There are 25 discs numbered 1 to 25. They are put in a closed box and shaken thoroughly. A disc is drawn at random from the box.

Find the probability that the number on the disc is :

(i) an odd number

(ii) divisible by 2 and 3 both

(iii) a number less than 16.

**Answer :**

(a) Sample space = 25 discs numbered from 1 to 25.

**(i) Odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25**

Probability (an odd number) = (13/25) .

##### (ii) **Numbers** divisible by 2 and 3 both are 6, 12, 18, 24

Probability (divisible by 2 and 3 both) = (4/25)

Numbers less than 16 are 1 to 15

**(iii) Probability (a no. less than 16)**

= (15/25) or (3/5)

**Probability Exe-22**

### ML Aggarwal Probability MCQs Class 10 ICSE Maths Solutions Ch-22

**Page 542**

**Question 21. ****A box contains 15 cards numbered 1, 2, 3,…..15 which are mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card is :**

**(i) Odd**

**(ii) prime**

**(iii) divisible by 3**

**(iv) divisible by 3 and 2 both**

**(v) divisible by 3 or 2**

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

**Answer :**

Number of cards in a box =15 numbered 1 to 15

**(i) Odd numbers are 1, 3, 5, 7, 9, 11, 13, 15**

Number of odd numbers = 8

Probability of odd numbers will be

P(E) = number of favourable outcome/number of possible outcome

= 8\15

**(ii) Prime number are 2, 3, 5, 7, 11, 13**

Number of primes is 6

Probability of prime number will be

P(E) = number of favourable outcome/number of possible outcome

= 6\15

= 2\5

**(iii) Numbers divisible by 3 are 3, 6, 9, 12, 15**

which are 5 in numbers

Probability of number divisible by 3 will be

P(E) = number of favourable outcome/number of possible outcome

= 5\15

= 1\3

**(iv) Divisible by 3 and 2 both are 6, 12**

which are 2 in numbers.

Probability of number divisible by 3 and 2

Both will be = 2\15

**(v) Numbers divisible by 3 or 2 are**

2, 3, 4, 6, 8, 9, 10, 12, 14, 15 which are 10 in numbers

Probability of number divisible by 3 or 2 will be

P(E) = number of favourable outcome/number of possible outcome

= 10\15

= 2\3

**(v) Perfect squares number are 1, 4, 9 i.e., 3 number**

P(E) = number of favourable outcome/number of possible outcome

= 3\15

= 1\5

**Question 22. **Cards bearing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card which is :

(i) a prime number.

(ii) a number divisible by 4.

(iii) a number that is a multiple of 6.

(iv) an odd number.

**Answer :**

Total number of cards in the bag = 10

**(i) Total prime numbers = 1 i.e., 2**

∴ Required Probability = (1/10)

**(ii) Total numbers divisible by 4 = 5 (i.e., 4, 8, 12, 16, 20]**

Required Probability = (5/10) = (1/2)

**(iii) Total numbers divisible by 6 or multiple of 6 = 3 [i.e., 6, 12, 18]**

∴ Required Probability = (3/10)

**(iv) Total odd number = 0**

∴ Required Probability = (0/10) = 0.

**Question 23. ****Cards marked with numbers 13, 14, 15, …, 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the number on the card drawn is**

**(i) divisible by 5**

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

**Answer :**

Number of card bearing numbers 13,14,15, … 60 = 48

One card is drawn at random.

**(i) Card divisible by 5 are 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 = 10**

Probability = 10/48

= 5/24

**(ii) A perfect square = 16, 25, 36, 49 = 4**

Probability = 4/48

= 1\12

**Question 24. ****Tickets numbered 3, 5, 7, 9,…., 29 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is**

**(i) a prime number**

**(ii) a number less than 16**

**(iii) a number divisible by 3.**

**Answer :**

In a box there are 14 tickets with number

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29

Number of possible outcomes = 14

**(i) Prime numbers are 3, 5, 7, 11, 13, 17, 19, 23, 29**

which are 9 in number

Probability of prime will be

P(E) = number of favourable outcome/number of possible outcome

= 9\14

**(ii) Number less than 16 are 3, 5, 7, 9, 11, 13, 15**

which are 7 in numbers,

Probability of number less than 16 will be

P(E) = number of favourable outcome/number of possible outcome

= 7\14

= 1\2

**(iii) Numbers divisible by 3 are 3, 9, 15, 21, 27**

which are 5 in number

Probability of number divisible by 3 will be

P(E) = number of favourable outcome/number of possible outcome

= 5\14

**Question 25. ****A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears**

**(i) a two-digit number**

**(ii) a perfect square number**

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

**Answer :**

There are 90 discs in a box containing numbered from 1 to 90.

Number of possible outcomes = 90

**(i) Two digit numbers are 10 to 90 which are 81 in numbers.**

Probability of two digit number will be

P(E) = number of favourable outcome/number of possible outcome

= 81/90

= 9/10

**(ii) Perfect squares are 1, 4, 9, 16, 25, 36,49, 64, 81**

which are 9 in numbers.

Probability of square will be

P(E) = number of favourable outcome/number of possible outcome

= 9\90

= 1\10

**(iii) Number divisible by 5 are**

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90

which are 18 in numbers.

Probability of number divisible by 5 will be

P(E) = number of favourable outcome/number of possible outcome

= 18\90

= 1\5

**Question 26. ****A bag contains 15 balls of which some are white and others are red. If the probability of drawing a red ball is twice that of a white ball, find the number of white balls in the bag.**

**Answer :**

In a bag, there are 15 balls.

Some are white and others are red.

Probability of red ball = 2 probability of white ball

Let number of white balls = x

Then, number of red balls = 15 – x

⇒ 2(15 – x) = x

and ⇒ 30 – 2x = x

so ⇒ 30 = x + 2x

Hence ⇒ x = 30/3 = 10

Number of red balls = 10

and Number of white balls = 15 – 10 = 5

**Question 27. ****A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball is twice that of a red ball, find the number of balls in the bag.**

**Answer :**

In a bag, there are 6 red balls, and some blue balls

Probability of blue ball = 2 × probability of red ball

Let number of blue balls = x

and number of red balls = 6

Total balls = x + 6

Probability of a blue ball = 2

⇒

and ⇒

Hence ⇒ x = 12

Number of balls = x + 6 = 12 + 6 = 18

**Question 28. ****A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A blue is selected at random. Find the probability that it is**

**(i) white**

**(ii) not red.**

**Answer :**

**(i) The number of favourable outcomes of the ball drawn is white = 8.**

∴ The probability that the drawn ball is white

= =

**(ii) In a bag, there are 24 balls**

Since, there are x balls red, 2 × balls white and 3 × balls blue

x + 2x + 3x = 24

6x = 24

x = 24/6

x = 4

Number of red balls = x

= 4

Number of white balls = 2x

= 2(4)

= 8

Number of blue balls = 3x

= 3(4)

= 12

The probability of selecting a ball that is not red is given by

Favourbale outcomes = balls other than red

= white balls + blue balls

Number of favourable outcomes = 8 + 12 = 20

Number of possible outcomes = 24

Probability = number of favourable outcomes / number of possible outcomes

Probability = 20/24

= 10/12

= 5/6

Therefore, the probability of selecting a ball that is not red is 5/6.

**Question 29. ****A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting:**

**(i) ‘2’ of spades**

**(ii) a jack .**

**(iii) a king of red colour**

**(iv) a card of diamond**

**(v) a king or a queen**

**(vi) a non-face card**

**(vii) a black face card**

**(viii) a black card**

**(ix) a non-ace**

**(x) non-face card of black colour**

**(xi) neither a spade nor a jack**

**(xii) neither a heart nor a red king**

**Answer :**

In a playing card, there are 52 cards

Number of possible outcome = 52

**(i) Probability of‘2’ of spade will be**

##### P(E) = number of favourable outcome/number of possible outcome

= 1/52

**(ii) There are 4 jack card Probability of jack will be**

##### P(E) = number of favourable outcome/number of possible outcome

= 4\52

= 1/13

**(iii) King of red colour are 2 in number**

Probability of red colour king will be

##### P(E) = number of favourable outcome/number of possible outcome

= 2\52

= 1\26

**(iv) Cards of diamonds are 13 in number**

Probability of diamonds card will be

##### P(E) = number of favourable outcome/number of possible outcome

= 13/52

= 1\4

**(v) Number of kings and queens = 4 + 4 = 8**

##### P(E) = number of favourable outcome/number of possible outcome

= 8/52

= 2\13

**(vi) Non-face cards are = 52 – 3 × 4 = 52 – 12 = 40**

Probability of non-face card will be

##### P(E) = number of favourable outcome/number of possible outcome

= 40\52

= 10/13

**(vii) Black face cards are = 2 × 3 = 6**

Probability of black face card will be

##### P(E) = number of favourable outcome/number of possible outcome

= 6/52

= 3/26

**(viii) No. of black cards = 13 x 2 = 26**

Probability of black card will be

##### P(E) = number of favourable outcome/number of possible outcome

= 26/52

= 1\2

**(ix) Non-ace cards are 12 × 4 = 48**

Probability of non-ace card will be

##### P(E) = number of favourable outcome/number of possible outcome

= 28\52

= 12\13

**(x) Non-face card of black colours are 10 × 2 = 20**

Probability of non-face card of black colour will be

##### P(E) = number of favourable outcome/number of possible outcome

= 20\52

= 5/13

**(xi) Number of card which are neither a spade nor a jack**

= 13 × 3 – 3 = 39 – 3 = 36

Probability of card which is neither a spade nor a jack will be

##### P(E) = number of favourable outcome/number of possible outcome

= 36/52

= 9\13

**(xii) Number of cards which are neither a heart nor a red king**

= 3 × 13 = 39 – 1 = 38

Probability of card which is neither a heart nor a red king will be

##### P(E) = number of favourable outcome/number of possible outcome

= 38\52

= 19\26

**Question 30. ****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**

**(iv) a heart**

**(v) a spade**

**(vi) ‘9’ of black colour**

**Answer :**

In a pack of 52 cards

All the three face cards of spade are = 3

Number of remaining cards = 52 – 3 = 49

One card is drawn at random

**(i) Probability of a black face card which are = 6 – 3 = 3**

Probability = 3\49

(ii) Probability of being a queen which are 4 – 1 = 3

Probability = 3\49

**(iii) Probability of being a black card = (26 – 3 = 23)**

Probability =

**(iv) Probability of being a heart = **

**(v) Probability of being a spade = (13 – 3 = 10)**

Probability =

**(vi) Probability of being 9 of black colour (which are 2) = **

**Question 31. ****From a pack of 52 cards, a blackjack, a red queen and two black kings fell down. A card was then drawn from the remaining pack at random. Find the probability that the card drawn is**

**(i) a black card**

**(ii) a king**

**(iii) a red queen.**

**Answer :**

In a pack of 52 cards, a blackjack, a red queen, two black being felt down.

Then number of total out comes = 52 – (1 + 1 + 2) = 48

(i) Probability of a black card (which are 26 – 3 = 23) =

(ii) Probability of a being (4 – 2 = 2) = =

(iii) Probability of a red queen = (2 – 1 = 1) =

**Probability Exe-22**

### ML Aggarwal Probability MCQs Class 10 ICSE Maths Solutions Ch-22

**Page 543**

**Question 32. ****Two coins are tossed once. Find the probability of getting:**

**(i) 2 heads**

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

**Answer 32**

Total possible outcomes are . HH, HT, TT, TH, i.e., 4

**(i) Favourable outcomes are HH, i.e., 1**

So, P(2 heads)

P(E) = number of favourable outcome/number of possible outcome

= 1/4

**(ii) Favourable outcomes are HT, TT, TH, i.e., 3**

So, P (at least one tail) = 3\4

**Question 33. ****Two different coins are tossed simultaneously. Find the probability of getting :**

**(i) two tails**

**(ii) one tail**

**(iii) no tail**

**(iv) almost one tail.**

**Answer :**

Two different coins are tossed simultaneously

Number of possible outcomes = (2)² = 4

Number of event having two tails = 1 i.e. (T, T)

**(i) Probability of two tails will be**

P(E) = number of favourable outcome/number of possible outcome

= 1\4

**(ii) Number of events having one tail = 2 i.e. (TH) and (HT)**

Probability of one tail will be

P(E) = number of favourable outcome/number of possible outcome

= 1/4

**(iii) Number of events having no tail = 1 i.e. (HH)**

Probability of having no tail will be

P(E) = number of favourable outcome/number of possible outcome

= 1/4

**(iv) Atmost one tail**

Number Of events having at the most one tail = 3 i.e. (TH), (HT, (TT)

Probability of at the most one tail will be

P(E) = number of favourable outcome/number of possible outcome

= 3\4

**Question 34. ****Two different dice are thrown simultaneously. Find the probability of getting:**

**(i) a number greater than 3 on each dice**

**(ii) an odd number on both dice.**

**Answer :**

When two different dice are thrown simultaneously,

then the sample space S of the random experiment =

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) .

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

It consists of 36 equally likely outcomes.

**(i) Let E be the event of ‘a number greater than 3 on each dice’.**

E = {(4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}

No. of favorable outcomes (E) = 9

P (number greater than 3 on each dice) = 9/36 = 1/4

**(ii) Let E be the event of ‘an odd number on both dice’.**

E = {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)}

No. of favourable outcomes (E) = 9

∴ P (Odd on both dices) = 9/36 = 1/4

**Question 35. ****Two different dice are thrown at the same time. Find the probability of getting :**

**(i) a doublet**

**(ii) a sum of 8**

**(iii) sum divisible by 5**

**(iv) sum of at least 11.**

**Answer :**

Two different dice are thrown at the same time

Possible outcomes will be (6)² i.e. 36

**(i) Number of events which doublet = 6**

i.e. (1, 1), (2, 2) (3, 3), (4, 4), (5, 5) and (6, 6)

.’. Probability of doublets will be

P(E) = number of favourable outcome/number of possible outcome

= 6/36

= 1/6

**(ii) Number of event in which the sum is 8 are**

(2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5

Probability of a sum of 8 will be

P(E) = number of favourable outcome/number of possible outcome

= 5/36

**(iii) Number of event when sum is divisible by**

5 are (1, 4), (4, 1), (2, 3), (3, 2), (4, 6),

(5, 5) = 7 in numbers

Probability of sum divisible by 5 will be

P(E) = number of favourable outcome/number of possible outcome

= 7/36

**(iv) Sum of atleast 11, will be in following events**

(5, 6), (6, 5), (6, 6)

Probability of sum of at least 11 will be

P(E) = number of favorable outcome/number of possible outcome

= 3/36

= 1/12

— : End of ML Aggarwal Probability Exe-22 Class 10 ICSE Maths Solutions Ch-22 : –

Return to :- ML Aggarwal Solutions for ICSE Class-10

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