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

What is the probability of getting a sum of 12 or more when rolling two fair six-sided dice?

  1. 1/6

  2. 1/3

  3. 1/2

  4. 2/3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are 36 possible outcomes when rolling two six-sided dice. The outcomes that sum to 12 or more are (6, 6), (5, 6), (6, 5), (4, 6), (6, 4), (3, 6), (6, 3), (2, 6), (6, 2). Therefore, the probability of getting a sum of 12 or more is 9/36, which simplifies to 1/4.

Multiple choice

What is the probability of getting a sum of 7 or 11 when rolling two fair six-sided dice?

  1. 1/4

  2. 1/6

  3. 1/8

  4. 1/12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are 36 possible outcomes when rolling two six-sided dice. The outcomes that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). The outcomes that sum to 11 are (5, 6), (6, 5). Therefore, the probability of getting a sum of 7 or 11 is (6 + 2)/36 = 8/36, which simplifies to 1/6.

Multiple choice

What is the probability of getting a sum of 13 or more when rolling two fair six-sided dice?

  1. 0

  2. 1/6

  3. 1/4

  4. 1/3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 36 possible outcomes when rolling two six-sided dice. The highest possible sum is 12. Therefore, the probability of getting a sum of 13 or more is 0.

Multiple choice

What is the probability of getting at least one head when flipping two fair coins?

  1. 1/4

  2. 1/2

  3. 3/4

  4. 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of getting at least one head is the complement of the probability of getting no heads. The probability of getting no heads is (1/2) * (1/2) = 1/4. Therefore, the probability of getting at least one head is 1 - 1/4 = 3/4.

Multiple choice

What is the probability of getting a sum of 11 when rolling two fair dice?

  1. 1/6

  2. 1/12

  3. 1/18

  4. 1/24
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of getting a sum of 11 when rolling two fair dice is 1/18.

Multiple choice

In the 2013 China Girls' Mathematical Olympiad, what was the probability of rolling a 6 on a standard six-sided die?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

There are six possible outcomes when rolling a standard six-sided die: 1, 2, 3, 4, 5, and 6. Therefore, the probability of rolling a 6 is 1 / 6.

Multiple choice

A box contains 15 balls. Out of these balls, five are of different colours and the rest are of white colour. Five balls are drawn at random from the box. What is the probability that four balls are coloured and one is white?

  1. 25 1001

  2. 35 2002

  3. 45 2121

  4. 50 3003

  5. 100 3003
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total number of ways to choose 5 balls from 15 is 15C5 = 3003. The number of ways to choose 4 coloured balls from 5 is 5C4 = 5, and 1 white ball from 10 is 10C1 = 10. The probability is (5 * 10) / 3003 = 50 / 3003.

Multiple choice

From a pack of 52 playing cards, five cards fall down - ten, jack, queen, king and ace of diamonds. After that, a card is drawn from the pack at random. What is the probability the card drawn is a face card?

  1. 5 47

  2. 9 47

  3. 3 47

  4. 7 47
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Five cards are removed, leaving 47 cards. The original deck had 12 face cards (J, Q, K of each suit). The removed cards were J, Q, K of diamonds (3 face cards). Remaining face cards = 12 - 3 = 9. The probability is 9/47.