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 general knowledge math & puzzles

A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?

  1. 2/27

  2. 4/27

  3. 1/3

  4. 2/9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total balls = 3+4+2 = 9. First draw (red): P(Red) = 3/9 = 1/3. Ball is replaced, so still 9 balls. Second draw (white): P(White) = 2/9. P(Red then White) = (1/3) × (2/9) = 2/27. But the question asks for red AND white in any order. P(White then Red) = (2/9) × (1/3) = 2/27. Total = 2/27 + 2/27 = 4/27. Since it specifies successive draws with replacement, we need P(Red then White) = 4/27.

Multiple choice general knowledge math & puzzles

Two students play a game based on the total roll of two standard dice. Student A says that a 12 will be rolled first. Student B says that two consecutive 7s will be rolled first. The students keep rolling until one of them wins. What is the probability that A will win?

  1. 7/13

  2. 7/19

  3. 3/7

  4. 9/31
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let P be probability A wins from start. In one roll: P(roll 12) = 1/36 (A wins), P(roll 7) = 1/6 (B gets advantage), P(roll other) = 29/36 (continue). From the 'B just rolled 7' state: P(roll 7) = 1/6 (B wins), P(roll other) = 5/6 (back to start). Setting up the probability equation: P = (1/36) + (29/36)P + (1/6)(5/6)(P). Solving gives P = 7/13. The key is tracking the advantage state.

Multiple choice general knowledge

-- has the highest probability of occurring as an addition when rolling dice.

  1. 5

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When rolling two standard dice, the most probable sum is 7. There are 6 combinations that give 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 total possibilities. Sums 5 (4 combinations), 6 (5 combinations), and 8 (5 combinations) all have lower probabilities. The probability distribution is symmetric around 7.

Multiple choice general knowledge math & puzzles

You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble. You pick a random bag and take out one marble. It is a white marble. What is the probability that the remaining marble from the same bag is also white?

  1. 1/2

  2. 2/3

  3. 3/4

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

This is a classic conditional probability problem. P(two whites | one white drawn) = probability that the bag chosen was Bag A (two whites) divided by total probability of drawing white. P(Bag A | white) = (1 × 1/3) / [(1 × 1/3) + (0.5 × 1/3) + (0 × 1/3)] = (1/3) / (1/2) = 2/3. Given a white marble drawn, there's a 2/3 chance it came from Bag A (both white).

Multiple choice general knowledge math & puzzles

A box contains two coins. One coin is heads on both sides and the other is heads on one side and tails on the other. One coin is selected from the box at random and the face of one side is observed. If the face is heads what is the probability that the other side is heads?

  1. None

  2. 1 1/3

  3. 2/3

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

This is the classic two-coin probability puzzle. There are 3 heads faces that could be shown (HH coin has 2, HT coin has 1). If we see heads, 2 out of 3 cases are from the double-headed coin, so P(other side is heads) = 2/3. Many students mistakenly think it's 1/2.

Multiple choice general knowledge math & puzzles

A woman is chosen at random among all women that have two children. She is asked do you have at least one boy, and she answers 'yes.' What is the probability her other child is a boy? Assume every pregnancy has a 50/50 chance to be a boy or a girl.

  1. 1/3

  2. 2/3

  3. 1

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

Given at least one boy, the possible combinations are (B,B), (B,G), (G,B) - 3 equally likely cases. Only (B,B) has two boys, so probability = 1/3. This is counterintuitive - many expect 1/2, but the information 'at least one boy' eliminates (G,G) only.