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

A coin is tossed 3 times Quantity A The number of possible outcomes containing exactly 2 heads Quantity B The number of possible outcomes containing exactly 1 tail

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Outcomes for 3 tosses: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. Exactly 2 heads: HHT, HTH, THH (3 outcomes). Exactly 1 tail: HHT, HTH, THH (3 outcomes). Both are 3.

Multiple choice

Two dice are rolled one by one. In how many ways is the sum of numbers, occurring on dice, a number of the form u2 + 1 where u is a natural number?

  1. 4

  2. 6

  3. 8

  4. 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The possible sums of two dice range from 2 to 12. The numbers of the form u^2 + 1 are 1^2+1=2, 2^2+1=5, and 3^2+1=10. The ways to get 2 are (1,1); to get 5 are (1,4), (2,3), (3,2), (4,1); to get 10 are (4,6), (5,5), (6,4). Counting these gives 1 + 4 + 3 = 8 ways.

Multiple choice

Two bags A and B contain 7 red and 6 blue balls respectively. Some blue balls from bag B are taken out and kept into bag A. If probability of selecting two blue ball from bag A is 1/15, find the number of blue balls drawn from bag B.

  1. 2

  2. 4

  3. 3

  4. 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the number of blue balls moved from B to A. Bag A now has 7 red and x blue balls (total 7+x). Probability of 2 blue balls = [x/(7+x)] * [(x-1)/(6+x)] = 1/15. Solving x(x-1) / (x^2 + 13x + 42) = 1/15 gives 15x^2 - 15x = x^2 + 13x + 42, so 14x^2 - 28x - 42 = 0, or x^2 - 2x - 3 = 0. Roots are x=3 and x=-1. Thus, x=3.

Multiple choice

Directions: Study the following information and answer the question given below. There are 6 children sitting in a park. Each of them has an identical coin. They all toss their coins together. What is the probability of getting 2 heads?

  1. 15 64

  2. 15 24

  3. 15 32

  4. 15 16

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

There are C(6,2) ways to choose which two children get heads. Each of the 6 coins has two possible outcomes, so there are 2^6 = 64 total outcomes. The probability is C(6,2)/64 = 15/64.

Multiple choice

A bag contains 5 white and 3 black balls. 4 balls are successively drawn out of the bag and are not replaced. What is the chance of getting different colours alternatively?

  1. 1/6

  2. 1/5

  3. 1/4

  4. 1/7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total balls = 8. Drawing 4 balls without replacement. To get different colors alternatively, the sequences must be W-B-W-B or B-W-B-W. Probability of W-B-W-B = (5/8)(3/7)(4/6)(2/5) = 120/1680 = 1/14. Probability of B-W-B-W = (3/8)(5/7)(2/6)(4/5) = 120/1680 = 1/14. Total probability = 1/14 + 1/14 = 2/14 = 1/7.

Multiple choice

Each of two persons tosses three fair coins. The probability that they obtain the same number of heads, is

  1. 1/2

  2. 5/16

  3. 7/16

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

Each person tosses 3 coins. The probability distribution for heads is: 0 heads (1/8), 1 head (3/8), 2 heads (3/8), 3 heads (1/8). The probability they get the same number of heads is the sum of the squares of these probabilities: (1/8)^2 + (3/8)^2 + (3/8)^2 + (1/8)^2 = (1 + 9 + 9 + 1) / 64 = 20 / 64 = 5/16.