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 6 identical cubes, with each face coloured differently. What is the probability that each cube will show a different coloured face on top, if thrown simultaneously?

  1. 12/325

  2. 52/325

  3. 5/324

  4. 2/325

  5. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Each cube has 6 faces. Total outcomes for 6 cubes is 6^6. Favorable outcomes where each shows a different face is 6! (permutations of 6 colors). Probability = 6! / 6^6 = 720 / 46656 = 5 / 324.

Multiple choice

There are four target balloons. Shooter decides to shoot randomly to hit the target. The probability of hitting a balloon successfully is 1/4. If he is allowed up to four chances to shoot the target, then find the probability that he will hit exactly three balloons.

  1. 3/64

  2. 1/16

  3. 1/8

  4. 3/7

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

The probability of hitting a balloon is p = 1/4, and missing is q = 3/4. For exactly 3 hits in 4 chances, we use the binomial distribution formula: C(4,3) * (1/4)^3 * (3/4)^1. This equals 4 * (1/64) * (3/4) = 12/256 = 3/64.

Multiple choice

Bag A contains three black balls and one white ball, Bag B contains two black balls and two white balls, Bag C contains one black ball and three white balls. One ball is drawn randomly from each bag. What is the probability that one of them is black and the other two are white?

  1. 3/32

  2. 13/32

  3. 1/32

  4. 3/2

  5. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of drawing one black and two white balls is the sum of the probabilities of three mutually exclusive scenarios: (B, W, W), (W, B, W), and (W, W, B). Bag A: P(B)=3/4, P(W)=1/4. Bag B: P(B)=2/4, P(W)=2/4. Bag C: P(B)=1/4, P(W)=3/4. Calculating: (3/4 * 2/4 * 3/4) + (1/4 * 2/4 * 3/4) + (1/4 * 2/4 * 1/4) = 18/64 + 6/64 + 2/64 = 26/64 = 13/32.

Multiple choice

In a dice game, if a player rolls two dice, then his score will be the larger of the two numbers on the dice and if he rolls a doublet, his score will be the same number as the number in doublet. For example, if he rolls 4 and 6, his score will be 6 and if he rolls a doublet, e.g. 3 and 3, then his score will be 3. What is the probability that his score is 4 or more?

  1. 1 4

  2. 7 36

  3. 5 36

  4. 3 4

  5. 1 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The score is less than 4 only when both dice show numbers from 1 to 3. There are 3 x 3 = 9 such outcomes out of 36, so the probability of a score of at least 4 is 1 - 9/36 = 3/4.

Multiple choice

Directions: The following question has four choices, out of which ONLY ONE is correct. A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw?

  1. 18

  2. 45

  3. 64

  4. 72

  5. 52
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 2+3+4 = 9. Total ways to draw 3 balls = 9C3 = 84. Ways to draw 3 balls with no black balls (only white/red) = 6C3 = 20. Ways with at least one black ball = 84 - 20 = 64.

Multiple choice

In a game, a person has to select three cards from a deck of cards. If he selects a face card, then the other two cards also have to be face cards. If a number card is selected, then all the other cards have to of the same number. In how many different ways can the selection be made?

  1. 12C3 + 9 × 4C3

  2. 12C3 + 40C3

  3. 13C3 + 4C3

  4. 12C3 + 9 × 4!

  5. 14C3 + 9 × 4C3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 12 face cards. Selecting 3 face cards is 12C3. For number cards, there are 9 numbers (2-10), each with 4 suits. Selecting 3 cards of the same number is 4C3 for each number, so 9 * 4C3.