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

Which of the following events is independent?

  1. Drawing two cards with replacement from a pack of 52 cards and getting an ace

  2. Drawing two cards with replacement from 52 cards to first get a king then an ace.

  3. Tossing of two coins simultaneously twice to get 4 heads.

  4. Tossing of a coin and if the result is head, then rolling of a dice to get an even number.
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

An urn contains 10 white balls numbered 1 to 10. A ball is to be selected at random and placed aside. What is the probability that we get a ball numbered '3' in first three turns?

  1. 3/10

  2. 1/30

  3. 121/360

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of picking the ball numbered 3 in any of the first three turns is 1 - P(not picking 3 in 3 turns). P(not picking 3) = (9/10) * (8/9) * (7/8) = 7/10. So, P(picking 3) = 1 - 7/10 = 3/10.

Multiple choice

Cards marked with numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from the box. The probability that the number on the card is a prime number less than 20 is

  1. 12/25

  2. 8/25

  3. 4/25

  4. 2/25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total number of cards marked from 2 to 101 is 100. The prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19, which gives a total of 8 favorable outcomes. Therefore, the probability of drawing such a card is 8/100, which simplifies to 2/25.

Multiple choice

A dice is so biased that it is twice as likely to show an even number as an odd number when rolled. It is rolled twice. Find the probability that the sum of two numbers rolled is even.

  1. 4/9

  2. 5/9

  3. 2/3

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P(odd) = p, P(even) = 2p. p + 2p = 1 => p = 1/3. P(odd) = 1/3, P(even) = 2/3. Sum is even if both are odd or both are even. P(even sum) = P(O,O) + P(E,E) = (1/3 * 1/3) + (2/3 * 2/3) = 1/9 + 4/9 = 5/9.