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 bag contains 3 different white balls, 4 different black balls and 2 different red balls. Two balls are picked at random. Find the probability of picking (a) one white ball and one red ball, (b) no white ball, and (c) exactly one black ball.

  1. a - 1 6 , b - 5 36 , c - 5 12

  2. a - 5 6 , b - 21 36 , c - 5 9

  3. a - 1 6 , b - 5 12 , c - 5 9

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

Total balls = 9. Total ways to pick 2 = 9C2 = 36. (a) 1 white (3C1) and 1 red (2C1) = 3 * 2 = 6. Prob = 6/36 = 1/6. (b) No white (6 non-white balls) = 6C2 = 15. Prob = 15/36 = 5/12. (c) Exactly one black (4C1 * 5C1) = 20. Prob = 20/36 = 5/9.

Multiple choice

A bag contains 10 white and 6 black balls. 4 balls are successively drawn without replacement. What is the probability that they are alternatively of different colours?

  1. 81/728

  2. 90/728

  3. 18/728

  4. 638/728

  5. 1/728
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total ways to draw 4 balls = 16C4 = 1820. Favorable ways: (W,B,W,B) or (B,W,B,W). W,B,W,B = (10/16)(6/15)(9/14)(5/13) = 2700/43680. B,W,B,W = (6/16)(10/15)(5/14)(9/13) = 2700/43680. Total = 5400/43680 = 90/728.