# Probability - Aptitude Questions and Answers

Learn and practice the chapter "Probability" with these solved Aptitude Questions and Answers. Each question in the topic is accompanied by a clear and easy explanation, diagrams, formulae, shortcuts and tricks that help in understanding the concept.

## Use of Probability Questions

The questions and examples given in this section will be useful to all the freshers, college students and engineering students preparing for placement tests or any competitive exam like MBA, CAT, MAT, SNAP, MHCET, XAT, NMAT, GATE, Bank exams - IBPS, SBI, RBI, RRB, SSB, SSC, UPSC etc.

Practice with this online test to crack your placements and entrance tests!
1. A mother has 24 pairs of white socks and 18 pairs of grey socks for her twin children kept in a bag. In a hurry to send the children to school on time, she picks 3 socks randomly. What is the possibility of her picking up the matching pair?

 a. 1 108
 b. 1 36
 c. 7 36
d. 1

Explanation:

Since a pair has 2 socks in it and there are just two colours - White and grey, when the mother chooses 3 socks, he will surely select 2 socks of same color - be it grey or white.

So possibility = probability = 1

2. You have a well shuffled deck of 52 playing cards. Find the possibility of drawing a Queen or hearts?

 a. 1 26
 b. 1 13
 c. 4 13
 d. 17 52

Explanation:

 Probability = What we want Total
OR = add        AND = multiply

We want queen OR hearts
There are 4 queens and 13 hearts cards
Total 52 cards
Also 1 queen is queen of hearts.
 So probability = 4 + 13 - 1 = 4 52 52 52 13

Remember - This subtraction is needed as queen of hearts gets counted twice - once in 4 queens and once again in 13 hearts.

3. Ramesh has a garments shop. He currently has 6 black, 4 red, 2 white and 3 blue shirts of same size in the stock. He picks 2 shirts randomly for the display. What is the probability that either both shirts are white or blue?

 a. 1 105
 b. 1 35
 c. 4 105
 d. 1 15

Explanation:

 Probability = What we want Total
OR = add       AND = multiply

Both white OR both blue
Total shirts = 15
There are 2 white and 3 blue shirts
 Probability for 2 white shirts = 2 x 1 = 1 15 14 105
 Probability for 2 blue shirts = 3 x 2 = 1 15 14 35
 Total Probability = 1 + 1 = 4 105 35 105

Remember:
Here we reduce the denominator i.e. total number of shirts because once we remove a shirt from the box we do not put it back in the box.
So while removing the 2nd shirt, there are only 15 - 1 = 14 shirts in the box.

4. There are 2 yellow, 6 black, 4 grey and 8 red pebbles in a glass bowl. I pick one pebble randomly. What is the probability of me picking up a black or red pebble?

 a. 1 10
 b. 7 10
 c. 3 4
 d. 4 3

Explanation:

 Probability = What we want Total
OR = add       AND = multiply

We want black OR red pebble
There are 6 black and 8 red pebbles
Total pebbles = 2 + 6 + 4 + 8 = 20
 So probability = 6 + 8 = 7 20 20 10

5. There are 2 bags. One has 5 white and 3 black napkins. The other one has 4 white and 2 black napkins. Find the probability of picking up a white napkin.

 a. 9 14
 b. 31 48
 c. 1 2
d. 1

Explanation:

 Probability = What we want Total
OR = add       AND = multiply

Here, one probability is to find which bag is selected AND other is for white napkin from the selected bag.
 Probability of selecting 1 bag out of 2 bags = 1 2
Say it has 4 white and 2 black napkins.
 So, White napkin probability = 4 = 4 4+2 6
 So Probability 1 = 1 x 4 = 4 2 6 12
 Similarly, Probability 2 = 1 x 5 = 5 2 5+3 16
 Total probability of white napkin = 4 + 5 = 31 12 16 48