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
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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