Ncert – Class 10 – Probability– Hots Question

Question 1

A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size.
Kritika takes out a ball from the bag without looking into it. What is the probability that she
takes out the
(i) yellow ball?
(ii) red ball?
(iii) blue ball?

Solution

The number of possible outcomes = Number of balls in the bag = n(S) = 3.
(i) The number of outcomes favourable to the event Y = n(Y) = 1.
So, P(Y) = n(Y)/n(S) =1/3Similarly,
(ii) P(R) = 1/3and
(iii) P(B) = ⅓

Question 2

A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random
from the box, find the probability that it bears a perfect square number.

Solution

Total number of outcomes = 80
Perfect square numbers from 1 to 80 = 1 ,4, 9, 16, 25, 36, 49, 64
Therefore, favourable outcomes = 8
Probability of getting a perfect square number = 8/80 = 1/10.

Question 3

A box contains 5 white balls, 3 red balls, and 2 green balls. If three balls are drawn one by
one without replacement, what is the probability that all three balls are of different colors?

Solution

Calculate the probability of drawing a white ball first (5/10), then a red ball (3/9), and
finally a green ball (2/8). Multiply these three probabilities to find the probability that
all three balls are of different colors.
Probability= (5/10)(3/9)(2/8)= 1/24

Question 4

In class X, there are 35 boys and 25 girls. In the Mathematics period, 5 students randomly taken out of class one after another without making them entry into the class. Now find the probability that 5 of them are girls?

Solution

Total boys and girls= 35+25= 60
Probability for all 5 are girls will be (25/60)(24/59)(23/58)(22/57)(21/56)=
(17710/1820504)= 0.009(approx.)

Question 5

In a school, there are 500 students. A survey conducted in the school for the favourite
subject among Hindi, Mathematics and science. After survey it was found that 250 liked
Hindi as their favourite subject, 150 liked Mathematics as their favourite subject and 100
liked Science as their favourite subject. If three students picked from the school randomly,
then what is the probability that all three are of different student having different favourite
subject.

Solution

To calculate this probability, we’ll consider the following cases:
First student likes Hindi, second student likes Mathematics, third student likes
Science.
First student likes Hindi, second student likes Science, third student likes
Mathematics.
First student likes Mathematics, second student likes Hindi, third student likes
Science.
3
First student likes Mathematics, second student likes Science, third student likes
Hindi.
First student likes Science, second student likes Hindi, third student likes
Mathematics.
First student likes Science, second student likes Mathematics, third student likes
Hindi.
So, probability= 6× (250/500)×(150/500)×(100/500)= 6×(1/2)×(3/10)×(1/5)=9/50

Question 6

Two unbiased coins are tossed simultaneously. Find the probability of getting
(i) at least one head
(ii) at most one head
(iii) no head

Solution

(i) 3/4

(ii) 3/4

(iii) 1/4

Question 7

A bag contains cards numbered 1 to 49. Find the probability that the number on
the drawn card is
(i) an odd number
(ii) a multiple of 5
(iii) Even prime

Solution

(i) 25/49

(ii) 9/49

(iii) 1/49

Question 8

Two dice are tossed simultaneously. Find the probability of getting
(i) an even number on both dice.
(ii) the sum of two numbers more than 9

Solution

(i) 1/4

(ii) 1/6

Question 9

A bag contains 15 white and some black balls. If the probability of drawing a black
ball from the bag is thrice that of drawing a white ball, find the number of black balls
in the bag.

Solution

there are 45 black ballsin the bag

Question 10

Three different coins are tossed together. Find the probability of getting

i)exactly two heads ii) at least two heads iii) at least two tails.

Solution

Probability of getting at least two tails =4/8=1/2