Probability Questions Quiz for SBI Clerk Pre, IBPS Clerk Pre, IBPS RRB

Direction : Read the following questions carefully and choose the right answer.
1
There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected?
» Explain it
C
Total number of ways of selecting 3 students from 25 students = 25C3

Number of ways of selecting 1 girl and 2 boys = selecting 2 boys from 15 boys and 1 girl from 10 girls

⇒ Number of ways in which this can be done = 15C2 × 10C1

⇒ Required probability =  (15C2 × 10C1)
(25C3)

21
46

Hence, option C is correct.

2
Three dice are thrown together. Find the probability of getting a total of at least 6 ? 
» Explain it
C
Since one die can be thrown in six ways to obtain any one of the six numbers marked on its six faces

⇒ Total number of elementary events = 6 x 6 x 6 = 216

Let A be the event of getting a total of at least 6.Then Ā denotes the event of getting a total of less than 6 i.e. 3, 4, 5.

⇒ Ā = { (1,1,1), (1,1,2), (1,2,1), (2,1,1), (1,1,3),(1,3,1), (3,1,1), (1,2,2), (2,1,2), (2,2,1) }

So, favorable number of cases = 10

⇒ P(Ā) =  10
216

⇒ 1 – P (A) =  10
216

⇒ P(A) = 1 –  10
216

103
108

Hence, option (C) is correct.

3
A bag contains 6 pink and 5 yellow balls. One ball is drawn randomly. What is the probability that the ball drawn is Pink?
» Explain it
D
Probability of 1 Pink Ball =  6C1
11C1

6
11

Hence, option D is correct.
4
In a box there are 10 apples and 2/5th of the apples are rotten. If three apples are taken out from the box, what will be the probability that at least one apple is rotten.
» Explain it
B
Let rotten apples = 10 ×  2  = 4, others = 6
5

If 1 apple is rotten + 2 apples are other

= 4C1 × 6C2 = 60

If 2 apples are rotten + 1 apple is other

= 4C2 × 6C1 = 36

If 3 apples are rotten

= 4C3 = 4

Total outcomes = 10C3 = 120

Probability =  60 + 36 + 4
120

100  =  5
120 6

Hence, option B is correct.
5
A bag contains 5 yellow and 2 green and 3 red colour dice. If one dice from the bag are choosen at random, what is the probability that dice is either yellow or red colour?
» Explain it
B
Probability of 1 yellow dice =  5C1
10C1

Probability of 1 red dice =  3C1
10C1

Total outcomes =  5C1  +  3C1
10C1 10C1

5  +  3
10 10

8  =  4
10 5

Hence, option B is correct.