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

When two dice are thrown, the probability of getting equal numbers is
  1. $\dfrac{1}{6}$
  2. $\dfrac{1}{2}$
  3. $\dfrac{1}{4}$
  4. $\dfrac{1}{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When two dice are thrown, there are 6 * 6 = 36 total outcomes. The outcomes with equal numbers are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6), which are 6 outcomes. The probability is 6/36 = 1/6.

Multiple choice

Choose the correct alternative for each of the following. Cards each marked with one of the numbers $4, 5, 6, ...,20$ are placed in a box and mixed thoroughly. One card is drawn at random from the box. Then the probability of getting an even prime number is
  1. $0$
  2. $1$
  3. $ \displaystyle \frac{1}{2} $

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The numbers are 4, 5, 6, ..., 20. The total number of cards is 20 - 4 + 1 = 17. The only even prime number is 2. Since 2 is not in the set {4, 5, ..., 20}, the probability is 0.

Multiple choice

A symmetrical die is tossed twice. Getting a four is considered to be a success. The mean and variance of number of successes are
  1. $\cfrac { 2 }{ 3 } ,\ \cfrac { 5 }{ 18 } $
  2. $\cfrac { 1 }{ 3 } ,\ \cfrac { 5 }{ 18 } $
  3. $\cfrac { 1 }{ 3 } ,\ \cfrac { 7 }{ 18 } $
  4. $\cfrac { 2 }{ 3 } ,\ \cfrac { 7 }{ 18 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a binomial distribution with n=2 and p=1/6 (probability of getting a 4). Mean = np = 2 * (1/6) = 1/3. Variance = npq = 2 * (1/6) * (5/6) = 10/36 = 5/18.

Multiple choice

5 cards are drawn one after an other successively with replacement from a well shuffled pack of 52 cards. The probability that none is a spade is
  1. 1-$(\displaystyle \frac{3}{4})^{5}$
  2. $(\displaystyle \frac{3}{4})^{5}$
  3. $(\displaystyle \frac{1}{4})^{5}$
  4. 1-$(\displaystyle \frac{1}{4})^{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of drawing a spade is 13/52 = 1/4. The probability of NOT drawing a spade is 3/4. Since the cards are drawn with replacement, the probability that none of the 5 cards is a spade is (3/4)^5.

Multiple choice

In selecting 2 cards one at a time with replacement from pack of cards, the probability that the second card is a black card, given that the first card was a red card is
  1. $\displaystyle \frac{1}{13}$
  2. $\displaystyle \frac{1}{2}$
  3. $\displaystyle \frac{1}{39}$
  4. $\displaystyle \frac{1}{8}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the selection is with replacement, the events are independent. The probability of the second card being black is independent of the first card being red. There are 26 black cards in a 52-card deck, so the probability is 26/52 = 1/2.