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Probability Questions Quiz With Explanation For SBI PO Pre, IBPS PO Pre, SBI Clerk, IBPS Clerk, 2018

Directions : Read the following questions carefully and choose the right answer.
1
A box contains 21 balls numbered 1 to 21. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls are even numbered?
» Explain it
C
There are 10 even numbers in the group 1-21.

∴   The probability that the first ball is even numbered =  10
21
 

Since the ball is not replaced there are now 20 balls left, of which 9 are even numbered.

∴ The probability that the second ball is even numbered =  9
20

∴   Required probability =  10  ×  9  =  9  =  3
21 20 42 14

Hence, option C is correct.
 
2
There are 3 green, 4 orange and 5 white color bulbs in a bag. If a bulb is picked at random, what is the probability of having either a green or a white bulb?
» Explain it
B
Let E1, E2 be the event of picking a green bulb and white bulb respectively.

Total no. of bulbs in a bag = 3 + 4 + 5 = 12

E1 =  3  =  1
12 4

E2 =  5  =  5
12 12

P(E1 or E2) = P(E1) + P(E2)
=   1  +  5  =  2
4 12 3

Hence, option B is correct.
 
3
A box contains slips with numbers from 1 to 50 written on them. A slip is drawn and replaced. Then another slip is drawn and after replacing another slip is drawn. What is the probability that an even number appears on the first draw, an odd number on the second draw and a number divisible by 3 on the third draw? 
» Explain it
B
The probability of an even number appearing on the first draw is 1/2( since there are 25 even numbers in counting of 1 to 50).

The probability of an odd number appearing on the second draw is 1/2( since there are 25 odd numbers in counting of 1 to 50).

The probability of a number divisible by 3 appearing on the third draw is 16/50 ( since there are 16 numbers that are divisible by 3 while counting from 1 to 50.)

Since all these events have no relation with each other and no dependence either, and the slips are replaced, we can directly multiply the individual probabilities to get the resultant probability.

So, the probability of all the events taking place is

1  ×  1  ×  16  =  2
2 2 50 25

Hence, option B is correct.

4
When 4 fair coins are tossed together what is the probability of getting at least 3 heads?
» Explain it
C
When 4 fair coins are tossed simultaneously, the total number of outcomes is 24 = 16

At least 3 heads implies that one can get either 3 heads or 4 heads.

One can get 3 heads in 4C3 = 4 ways and can get 4 heads in 4C4 = 1 ways.

∴ Total number of favorable outcomes = 4 + 1 = 5

∴ The required probability =  1
4

Hence, option C is correct.

5
A committee of 3 members is to be made out of 6 men and 5 women. What is the probability that the committee has at least two women?
» Explain it
B
Number of possible combination of 3 persons in which 2 have to be women = (2 Women out of 5 x 1 Man out of 6) or (3 Women out of 5)

= (5C2 × 6C1 + 5C3)

Total possible outcomes = 11C3

=  
5!  ×  6!  +  5!
2! × 3! 5! × 1! 3! × 2!
 = 
70
11 × 15
 = 
14
33
11!
3! × 8!

Hence, option B is correct.