Quantitative Aptitude

Probability

1,860 Questions
All Sample Space Setup 558 Permutation & Combination Counting 288 Multiplication Theorem (AND) 234 Addition Theorem (OR) 151 At Least One Probability 134 Complement Rule (P(Not A)) 130 Drawing Without Replacement 126 Conditional Probability 75 Bayes' Theorem 69 Drawing With Replacement 49 Success and Failure Rates 46

Probability Questions

Multiple choice

There are two urns. One contains two white balls and four red balls, the other contains three white and nine red balls. All balls are of the same shape and size. From each urn, one ball is drawn. What is the probability of getting both the balls of the same colour?

  1. 1/24

  2. 7/12

  3. 1/12

  4. 1/2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Urn 1: P(W)=2/6=1/3, P(R)=4/6=2/3. Urn 2: P(W)=3/12=1/4, P(R)=9/12=3/4. Same color = (P(W1)*P(W2)) + (P(R1)*P(R2)) = (1/3 * 1/4) + (2/3 * 3/4) = 1/12 + 6/12 = 7/12.

Multiple choice

From a deck of playing cards, one card is removed randomly & found to be a Jack of hearts. Then a second card is drawn without replacing the first one. What is the probability of getting a second card as a Jack of red colour?

  1. 1/52

  2. 1/51

  3. 11/52

  4. 13/51

  5. 1/26
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original deck has 52 cards. One Jack of hearts is removed, leaving 51 cards. There are 4 Jacks total; one is gone, so 3 remain. Two are red (hearts, diamonds). Since the heart is gone, only the Jack of diamonds remains. Probability = 1/51.

Multiple choice

An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is

  1. 1 2

  2. 4 9

  3. 5 9

  4. 6 9

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a classic probability problem. Regardless of the first draw, the probability of drawing a red ball in the second draw remains 5/10 = 1/2 because the first ball's color is unknown.