## Probability Solved Questions For IBPS, SBI and Other Bank Exams - Page 3

**Question 1**

In a class, there are 12 boys and 16 girls. One of them is called out by an enroll number, what is the probability that the one called is a girl?

a) 1/4 b) 2/5 c) 5/12 d) 4/7

**Answer : **d) 4/7.

Solution :

Let S be the sample space.

Total number of students in the class = 12 boys + 16 girls = 28.

Then, n(S) = 28.

Let E be the event of calling one of them by enroll number.

Given that, number of girls = 16.

Then, n(E) = 16.

The probability that the one called is a girl = n(S)/n(E) = 16/28 = 4/7.

**Question 2**

A box contains 3 white, 4 red and 7 blue erasers. If five erasers are taken at random then the probability that all the five are blue color is:

a) 13/211 b) 2/126 c) 3/286 d) 12/121

**Answer : **c) 3/286

Solution :

Total number of erasers in the box = 3 + 4 + 7 = 14.

Let S be the sample space.

Then, n(S) = number of ways of taking 5 out of 14.

Therefore, n(S) = 14C5 = (14 x 13 x 12 x 11 x 10)/(2 x 3 x 4 x 5) = 14 x 13 x 11 = 2002

Let E be the event of getting all the 5 blue erasers.

Therefore, n(E) = 7C5 = (7 x 6 x 5 x 4 x 3)/(2 x 3 x 4 x 5) = 21.

Now, the required probability = n(E)/n(S) = 21/2002 = 3/286.

**Question 3**

A box contains 6 bottles of variety1 drink, 3 bottles of variety2 drink and 4 bottles of variety3 drink. Three bottles of them are drawn at random, what is the

probability that the three are not of the same variety?

a) 833/858 b) 752/833 c) 632/713 d) none of these

**Answer : **a) 833/858

Solution :

Total number of drink bottles = 6 + 3 + 4 = 13.

Let S be the sample space.

Then, n(S) = number of ways of taking 3 drink bottles out of 13.

Therefore, n(S) = 13C3 = (13 x 12 x 11)/(1 x 2 x 3) = 66 x 13 = 858.

Let E be the event of taking 3 bottles of the same variety.

Then, E = event of taking (3 bottles out of 6) or (3 bottles out of 3) or (3 bottles out of 4)

n(E) = 6C3 + 3C3 + 4C3

= 6 x 5 x 4 / 1 x 2 x 3 + 1 + 4 x 3 x 2 / 1 x 2 x 3

= 20 + 1 + 4 = 25.

The probability of taking 3 bottles of the same variety = n(E)/n(S) = 25/858.

Then, the probability of taking 3 bottles are not of the same variety = 1 - 25/858 = 833/858.

**Question 4**

There are 12 boys and 8 girls in a tution centre. If three of them scored first mark, then what is the probability that one of the three is a girl and the other two are boys?

a) 14/75 b) 22/55 c) 44/95 d) none of these

**Answer :** c) 44/95

Solution :

Total number of students = 20.

Let S be the sample space.

Then, n(S) = number of ways of three scored first mark

n(S) = 20C3 = 20 x 19 x 18 / 2 x 3 = 20 x 19 x 3

Let, E be the event of 1 girl and 2 boys.

Therefore, n(E) = number of possible of 1 girl out of 8 and 2 boys out of 12.

n(E) = 8C1 x 12C2 = 8 x 12 x 11 / 1 x 2 = 8 x 6 x 11.

Now, the required probability = n(E)/n(S) = (8 x 6 x 11)/(20 x 19 x 3) = 44/95.