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

In a set of 24 cards, each card is numbered with a different positive integer from 1 to 24. One card will be drawn at random from the set. What is the probability that the card drawn will have either a number that is divisible by both 2 and 3 or a number that is divisible by 7 ?

  1. 3/24

  2. 4/24

  3. 7/24

  4. 8/24

  5. 17/24
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Divisible by 2 and 3 (i.e., by 6): 6, 12, 18, 24 (4 numbers). Divisible by 7: 7, 14, 21 (3 numbers). Total unique numbers = 4 + 3 = 7. Probability = 7/24.

Multiple choice

A pair of fair 6-sided dice is rolled n times. What is the least value of n such that the probability that the sum of the numbers face up on a roll equals 7 at least once is greater than 1/2?

  1. 2

  2. 3

  3. 4

  4. 5

  5. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Probability of sum 7 in one roll is 6/36 = 1/6. Probability of not getting 7 in n rolls is (5/6)^n. We want 1 - (5/6)^n > 1/2, so (5/6)^n < 1/2. For n=3, (5/6)^3 = 125/216 approx 0.578. For n=4, (5/6)^4 = 625/1296 approx 0.482. Thus n=4 is the least value.

Multiple choice

Shawn has 9 one-dollar coins with him. What is the probability of obtaining at least five heads, when he tosses each coin once?

  1. 5 9

  2. 4 9

  3. 1 2

  4. 2 9

  5. 1 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The distribution of heads in 9 coin tosses is symmetric. The probability of getting at least 5 heads is equal to the probability of getting at least 5 tails. Since the total probability is 1, and the probability of getting exactly 4.5 heads is impossible, the probability of getting >= 5 heads is exactly 1/2.

Multiple choice

A marble is drawn at random from a box containing 4 red marbles and 6 white marbles. Column A Column B The probability that the marble is white 2/3 Compare the two quantities to decide whether

  1. the quantity in Column A is greater

  2. the quantity in Column B is greater

  3. the two quantities are equal

  4. the relationship cannot be determined from the information given
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Probability of white marble = 6 / (4+6) = 6/10 = 0.6. Column B is 2/3 = 0.666. Since 0.6 < 0.666, Column B is greater.

Multiple choice

There are three urns A, B and C Urn A contains 4 white balls and 5 blue balls. Urn B contains 4 white balls and 3 blue balls. Urn C contains 2 white balls and 4 blue balls. One ball is drawn from each of these urns. What is the probability that out of these three balls drawn, 2 are white balls and 1 is blue ball?

  1. 3/7

  2. 2/7

  3. 1/189

  4. 64/189
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Urn A: P(W)=4/9, P(B)=5/9. Urn B: P(W)=4/7, P(B)=3/7. Urn C: P(W)=2/6=1/3, P(B)=4/6=2/3. We need 2 white and 1 blue. Possible cases: (W,W,B) = (4/9)(4/7)(2/3) = 32/189; (W,B,W) = (4/9)(3/7)(1/3) = 12/189; (B,W,W) = (5/9)(4/7)(1/3) = 20/189. Total = (32+12+20)/189 = 64/189.