**Probability ICSE Class-8th Concise** Mathematics Selina Solutions Chapter-23 . We provide step by step Solutions of Exercise / lesson-23 **Probability** for **ICSE Class-8 Concise** Selina Mathematics.

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**Probability ICSE Class-8th Concise** Mathematics Selina Solutions Chapter-23

**Exercise – 23**

**Question 1 :-**

A die is thrown, find the probability of getting:

(i) a prime number

(ii) a number greater than 4

(iii) a number not greater than 4.

**Answer :-**

(i)

A die has six numbers: 1, 2, 3, 4, 5, 6

∴ Number of possible outcomes = 6

a number greater than 4

Numbers of favourable outcomes = greater than four i.e. two number 5 and 6

**= 2/6=1/3**

(ii)

A die has six numbers: 1, 2, 3, 4, 5, 6

∴ Number of possible outcomes = 6

a number greater than 4

Numbers of favourable outcomes = greater than four i.e. two number 5 and 6

**= 2/6=1/3**

(iii)

A die has six numbers: 1, 2, 3, 4, 5, 6

∴ Number of possible outcomes = 6

Number of favourable outcomes = not greater than 4 or numbers will be 1,2,3,4 which are 4 in numbers

**= 4/6=2/3**

#### Question 2 :-

A coin is tossed. What is the probability of getting:

(i) a tail? (ii) ahead?

**Answer :- **

(i)

On tossing a coin once,

Number of possible outcome = 2

Favourable outcome getting a tail = 1

⇒ number of Favourable outcome = 2

**= 1/2**

(ii)

On tossing a coin once,

Number of possible outcome = 2

a head

Similarly, Favourable outcome of getting a head = 1

But the number of possible outcomes = 2

**= 1/2**

**Question 3 :-**

A coin is tossed twice. Find the probability of getting:

(i) exactly one head (ii) exactly one tail

(iii) two tails (iv) two heads

**Answer :-**

**(i)**

Exactly one head

Possible number of favourable outcomes = 2 (i.e. TH and HT)

Total number of possible outcomes = 4

**= 2/4=1/2**

**(ii)**

Exactly one tail

Possible number of favourable outcomes = 2 (i.e. TH and HT)

Total number of possible outcomes = 4

**= 2/4=1/2**

**(iii)**

Two tails

Possible number of favourable outcomes = 1 (i.e. TT)

Total number of possible outcomes = 4

**= 1/4**

**(iv)**

Two heads

Possible number of favourable outcomes = 1 (i.e. HH)

Total number of possible outcomes = 4

**∴ P(E) = 1/4 **

**Question 4 :-**

A letter is chosen from the word ‘PENCIL’ what is the probability that the letter chosen is a consonant?

**Answer :-**

Total Number of Consonant = ‘PNCL’ i.e. 4

**Question 5 :-**

A bag contains a black ball, a red ball and a green ball, all the balls are identical in shape and size. A ball is drawn from the bag without looking into it. What is the probability that the ball drawn is:

(i) a red ball

(ii) not a red ball

(iii) a white ball.

**Answer:-**

Total number of possible outcomes = 3

**∴ P(E) = 1/3**

(ii)

Not a red ball

Number of favourable outcomes

= Green ball + Black ball

= 1 + 1 + 2

**∴ P(E) = 2/3**

(iii)

A white ball

Number of favourable outcomes = 0

∴ P(E) = 0/3=0

**Question 6 :-**

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

(i) greater than 2

(ii) less than or equal to 2

(iii) not greater than 2.

**Answer :-**

A die has six numbers = 1, 2, 3, 4, 5, 6

∴ Number of possible outcomes = 6

**∴ P(E) = 4/6=2/3**

(ii)

Less than or equal to 2

Number of favourable outcomes = 1,2

**∴ P(E) = 2/6=1/3**

(iii)

Not greater than 2

Number of favourable outcomes = 1,2

**∴ P(E) = 2/6=1/3**

**Question 7 :-**

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 :-**

**(i)**

In a bag, 3 balls are white

2 balls are red

5 balls are black

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

Number of possible outcomes of one black ball = 10

and the number of favourable outcomes of one black ball = 5

**= 5/10 = 1/2**

**(ii)**

In a bag, 3 balls are white

2 balls are red

5 balls are black

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

Number of possible outcomes of one red ball = 10

and the number of favourable outcomes = 2

**= 2/10=1/5**

**(iii)**

In a bag, 3 balls are white

2 balls are red

5 balls are black

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

Number of possible outcomes of white ball = 10

and the number of favourable outcomes = 3

**= 3/10**

**(iv)**

In a bag, 3 balls are white

2 balls are red

5 balls are black

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

Number of possible outcomes = 10

number of favourable outcomes = 3 + 5 = 8

not a red ball

**= 8/10 = 4/5**

**(v)**

In a bag, 3 balls are white

2 balls are red

5 balls are black

Total number of balls not a black ball = 3 + 2 + 5 = 10

Number of possible outcomes = 10

number of favourable outcomes not a black ball = 3 + 2 = 5

**= 5/10=1/2**

**Question 8 :-**

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

(i) will be an even number.

(ii) will be an odd number.

(iii) will not be an even number.

**Answer :-**

A die has six numbers: 1, 2, 3, 4, 5, 6

∴ Number of possible outcome = 6

(i) Number of favourable outcomes = an even number i.e. 2, 4, 6 which are 3 in numbers

**= 3/6=1/2**

(ii) & (iii) Number of favourable outcome = not an even number i.e. odd numbers : 1,3,5 which are 3 in numbers

**= 3/6=1/2**

**Question 9 :-**

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

(i) 8

(ii) a number greater than 8

(iii) a number less than 8

**Answer :-**

On a die, the numbers are 1, 2, 3, 4, 5, 6 i.e. six.

∴ Number of possible outcome = 6

(i)

Number of a favourable outcomes = 0 (∵ 8 is not possible)

= 0/6 = 0

(ii)

Number greater than 8 will be 0

= 0/6 = 0

(iii)

Number less than 8 will be 1,2,3,4,5,6

=6/6 = 1

**Question 10 :-**

Which of the following can not be the probability of an event?

(i) 2/7

(ii)3.8

(iii) 37%

(iv) -0.8

(v) 0.8

(vi) -2/5

(vii) 7/8

**Answer :-**

The probability of an event cannot be

(ii) 3.8 i.e. the probability of an event cannot exceed 1.

(iv) i.e. -0.8 and

(vi) -2/5, This is because the probability of an event can never be less than 1.

**Question 11 :-**

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 :-**

∵ There are 6 black balls in a bag

∴ number of possible outcome = 6

(i) A white ball

As there is no white ball in the bag

∴ Its probability is zero (0) = or P(E) = 0

(ii) a black ball

∴ Number of favourable outcome = 1

**= 1/6**

**Question 12 :-**

**Three identical coins are tossed together. What is the probability of obtaining:**

(i) all heads?

(ii) exactly two heads?

(iii) exactly one head?

(iv) no head?

**Answer :-**

**(i)**

Total outcomes = 8

i.e. (H,H,H),(H,H,T),(H,T,H),(T,T,T),(T,H,H),(T,T,H),(H,T,T),(T,H,T)

Favourable outcome = i.e. (H,H,H)

**∴ P(of getting all heads) = 1/8**

**(ii)**

Total outcomes = 8

i.e. (H,H,H),(H,H,T),(H,T,H),(T,T,T),(T,H,H),(T,T,H),(H,T,T),(T,H,T)

Favourable outcome = 3 (H,H,T) , (H,T,H) , (T,H,H)

**∴ P(E) = 3/8**

**(iii)**

Total outcomes = 8

i.e. (H,H,H),(H,H,T),(H,T,H),(T,T,T),(T,H,H),(T,T,H),(H,T,T),(T,H,T)

Favourable outcome = 3 (H,T,H) , (T,T,H) , (H,T,T)

**∴ P(E) = 3/8**

**(iv) **

Total outcomes = 8

i.e. (H,H,H),(H,H,T),(H,T,H),(T,T,T),(T,H,H),(T,T,H),(H,T,T),(T,H,T)

Favourable outcome = 1 i.e. (T,T,T)

**∴ P(E) = 1/8**

**Question 13 :-**

A book contains 92 pages. A page is chosen at random. What is the probability that the sum of the digits in the page number is 9?

**Answer :-**

Number of pages of the book = 92

Which are from 1 to 92

Number of possible outcomes = 92

∴ Number of pages whose sum of its page is 9 = 10

i.e. 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

**∴ P(E) = 10/92=5/46**

**Question 14 :-**

Two coins are tossed together. What is the probability of getting:

(i) at least one head

(ii) both heads or both tails.

**Answer :-**

∵ A coin has two faces Head and Tail or H, T

∴ Two coins are tossed

∴ Number of coins = 2 x 2 = 4

which are HH, HT, TH, TT

(i)

At least one head, then

Number of outcomes = 3

**= 3/4**

(ii)

When both head or both tails, then

Number of outcomes = 2

**2/4=1/2**

**Question 15 :-**

From 10 identical cards, numbered 1, 2, 3, …… , 10, one card is drawn at random. Find the probability that the number on the card drawn is a multiple of:

(i) 2 (ii) 3

(iii) 2 and 3 (iv) 2 or 3

**Answer :-**

**(i)**

Total outcomes = 10

i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Favourable outcomes = 5

i.e. 2,4,6,8,10

**P(E) = 5/10=1/2**

**(ii)**

Total outcomes = 10

i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Favourable outcomes = 3

i.e. 3,6,9

**P(E) = 3/10**

**(iii)**

Total outcomes = 10

i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Favourable outcomes = 1

i.e. 6

**P(E) = 1/10**

**(iv)**

Total outcomes = 10

i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Favourable outcomes = 7

i.e. 2,3,4,6,8,9,10

**P(E) = 7/10**

**Question 16 :-**

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) 0

(ii) 12

(iii) less than 12

(iv) less than or equal to 12

**Answer :-**

**(i)**

Total outcomes = 36 i.e.

(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)

Favourable outcomes = 0

**P(E) = 0/36=0**

**(ii)**

Total outcomes = 36 i.e.

(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)

Favourable outcomes = 1

i.e. (6,6)

**P(E) = 1/36**

**(iii)**

Total outcomes = 36 i.e.

(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)

Favourable outcomes = 35 [Except (6,6)]

**P(E) = 35/36**

**(iv)**

Total outcomes = 36 i.e.

(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)

Favourable outcomes = 36

**P(E) = 36/36=1**

**Question 17 :-**

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

(i) a prime number

(ii) a number greater than 3

(iii) a number other than 3 and 5

(iv) a number less than 6

(v) a number greater than 6.

**Answer :-**

**(i)**

Total outcomes = 6

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

Favourable outcomes = 3

i.e. 2,3,5

**P(E) = 3/6=1/2**

**(ii)**

Total outcomes = 6

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

Favourable outcomes = 3

i.e. 4,5,6

**P(E) = 3/6=1/2**

**(iii)**

Total outcomes = 6

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

Favourable outcomes = 4

i.e. 1,2,4,6

**P(E) = 4/6 = 2/3**

**(iv)**

Total outcomes = 6

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

Favourable outcomes = 5

i.e. 1,2,3,4, and 5

**P(E) = 5/6**

**(v)**

Total outcomes = 6

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

Favourable outcomes = 0

**P(E) = 0/6 = 0**

**Question 18 :-**

Two coins are tossed together. Find the probability of getting:

(i) exactly one tail

(ii) at least one head

(iii) no head

(iv) at most one head

**Answer :-**

**(i)**

Total outcomes = 4

i.e., HH, HT, TT, TH

Favourable outcomes = 2 i.e., HT and TH

**P(E) = 2/4 = 1/2**

**(ii)**

Total outcomes = 4

i.e., HH, HT, TT, TH

Favourable outcomes = 3

i.e., HH and HT & TH

**P(E) = 3/4**

**(iii)**

Total outcomes = 4

i.e., HH, HT, TT, TH

Favourable outcomes = 1

i.e., TT

**P(E) = 1/4**

**(iv)**

Total outcomes = 4

i.e., HH, HT, TT, TH

Favourable outcomes = 3

i.e., HH , HT and TH

**P(E) = 3/4**

— End of** Probability ICSE Class-8th Concise **Solutions :–

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