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

Peter has ten coloured cubes in a bag. Three of the cubes are red and seven are blue. He draws a cube at random from the bag and notes the colour. Then, without replacement, he randomly draws another cube. What is the probability that he selected a red cube after a blue cube?

  1. 0.233

  2. 0.249

  3. 0.264

  4. 0.278
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total cubes = 10. Blue = 7, Red = 3. P(Blue first) = 7/10. Remaining cubes = 9. P(Red second | Blue first) = 3/9 = 1/3. Total probability = (7/10) * (1/3) = 7/30 = 0.2333...

Multiple choice

There are 10 coloured beads in a bag. Out of them 3 are red, 5 are green and the remaining are blue. Two beads are picked one by one without replacement. What is the probability that first bead is green and second is red?

  1. 0.10

  2. 0.17

  3. 0.20

  4. 0.25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total beads = 10. Red = 3, Green = 5, Blue = 2. Probability(1st Green) = 5/10 = 1/2. Probability(2nd Red | 1st Green) = 3/9 = 1/3. Total probability = (1/2) * (1/3) = 1/6 = 0.1666... which rounds to 0.17.

Multiple choice

A basket contains 12 red, 10 black and 5 pink balls. 5 balls are drawn at random. The number of ways of drawing at least 2 black balls is

  1. 30,412

  2. 51,242

  3. 50,742

  4. 43,262
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 27. Total ways to draw 5 balls = 27C5 = 80730. Ways to draw 0 black = 17C5 = 6188. Ways to draw 1 black = 10C1 * 17C4 = 10 * 2380 = 23800. Ways to draw at least 2 black = Total - (0 black + 1 black) = 80730 - (6188 + 23800) = 50742.

Multiple choice

A fair coin is tossed a fixed number of items. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads is:

  1. 15/28

  2. 2/15

  3. 15/213

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

For a binomial distribution, P(X=k) = C(n,k) * p^k * (1-p)^(n-k). If p=0.5, P(X=7) = P(X=9) implies C(n,7) = C(n,9), so n = 7+9 = 16. The probability of 2 heads is C(16,2) * (0.5)^16 = (16*15/2) / 2^16 = 120 / 2^16 = 15 / 2^13.

Multiple choice

A ball is drawn from an urn containing one red ball and one black ball. If the ball drawn is red, a coin is tossed; if it is black, a die is rolled. What is the probability of getting a head?

  1. 1 / 2

  2. 1 / 12

  3. 1 / 4

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

The probability of picking a red ball is 1/2, and the probability of getting a head from a coin toss is 1/2. The probability of picking a black ball is 1/2, and the probability of getting a head from a die roll is 0. Thus, the total probability is (1/2 * 1/2) + (1/2 * 0) = 1/4.