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 science & technology

There are 2 bags. The 1st bag contains 3 RED and 2 BLACK ball. The 2nd bag contains 4 RED and 6 BLACK ball. if a man choses a bag at random and picks a ball then what is the probability that the ball is RED?

  1. 7/15

  2. 1/2

  3. 1/3

  4. 8/15
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is total probability theorem. P(Red) = P(choose bag 1) × P(Red|bag 1) + P(choose bag 2) × P(Red|bag 2) = (1/2) × (3/5) + (1/2) × (4/10) = 3/10 + 2/10 = 5/10 = 1/2. Each bag is equally likely to be chosen, then we combine the weighted probabilities.

Multiple choice general knowledge math & puzzles

Find the probability of getting number between 2 and 6 when the dice is thrown one time?

  1. 1

  2. 2/6

  3. 1/2

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

When a standard die is thrown once, there are 6 equally likely outcomes (1,2,3,4,5,6). The numbers 'between 2 and 6' (excluding endpoints) are 3, 4, and 5 - that's 3 favorable outcomes. Probability = 3/6 = 1/2. Option C is correct. Option B (2/6) would be incorrect, and option A (1) is impossible for probability.

Multiple choice general knowledge

I ask people at random if they have two children and also if one is a boy born on a tuesday. After a long search I finally find someone who answers yes. What is the probability that this person has two boys? Assume an equal chance of giving birth to either gender and an equal chance to giving birth on any day.

  1. 1/2

  2. 2/7

  3. 1/7

  4. 13/27
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is the classic conditional probability puzzle. The sample space is all 2-child families where at least one child is a boy born on Tuesday. There are 27 equally likely possibilities (7x7 - 1 + 7 for the double-counted BB-Tue/BB-Tue case). Of these, 13 have two boys (BB-Tue/BB-Tue + 12 others where one is BB-Tue and the other is a boy on a different day). Thus P(2 boys | at least 1 boy born Tuesday) = 13/27.

Multiple choice

For each element in a set of size 2n, an unbiased coin is tossed. The 2n coin tosses are independent. An element is chosen if the corresponding coin toss were head. The probability that exactly n elements are chosen is:
  1. $\frac{^{2n}\mathrm{C}_n}{4^n}$
  2. $\frac{^{2n}\mathrm{C}_n}{2^n}$
  3. $\frac{1}{^{2n}\mathrm{C}_n}$
  4. $\frac{1}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Required favourable cases = Number of ways of selecting n element out of the set of size 2n = $^{2n}\mathrm{C}_n$ As each toss may result in either head or tail, so for 2n tosses, total no. of combinations = 22n = 4n $\therefore$Required probability = $\dfrac{\text{Favourable cases}}{\text{Total cases}}$ $ = \frac{^{2n}\mathrm{C}_n}{4^n}$

Multiple choice

An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than 3 is 0.75, which one of the following options is closest to the probability that the face value exceeds 3?

  1. 0.453

  2. 0.468

  3. 0.485

  4. 0.492
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?

  1. 1/5

  2. 4/25

  3. 1/4

  4. 2/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(2, 1), (3, 2), (4, 3), (5, 4) Required probability = $\dfrac{4}{5\times4} = \dfrac{4}{20} = \dfrac{1}{5}$

Multiple choice

A fair dice is rolled twice. The probability that an odd number will follow an even number is
  1. $\dfrac{1}{2}$
  2. $\frac{1}{6}$
  3. $\frac{1}{3}$
  4. $\frac{1}{4}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Probability of coming odd number is $\frac{1}{2}$ and the probability of coming even number is $\frac{1}{2}$. Both the events are independent to each other, thus probability of coming odd number after as even number is $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$