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Quantitative Aptitude · Bank exam practice

Probability questions for bank exams

Probability questions use coins, dice, cards, balls in bags and people in arrangements. Plutomonk has 1,040 Probability questions in Prelims and Mains sets of 10, each with a worked solution. They are useful for IBPS PO, SBI PO, IBPS Clerk, SBI Clerk, IBPS RRB and RBI Assistant.

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Quick tip

Count favourable outcomes with nCr and divide by the total. Check whether picks are with or without replacement.

Probability sample questions with answers

These are from the first Prelims and Mains sets. Try each question before you open the solution.

Q1. A bag contains 7 red, 6 blue and 3 green balls. One ball is drawn at random. What is the probability that it is green?

  1. 3/13
  2. 3/16
  3. 1/4
  4. 1/16
  5. 3/17
Show answer and solution

Answer: B. 3/16

Favourable = 3, total = 16. P = 3/16.

Q2. A bag contains 8 red, 4 blue and 7 green balls. One ball is drawn at random. What is the probability that it is red?

  1. 9/19
  2. 1/19
  3. 8/19
  4. 11/19
  5. 2/5
Show answer and solution

Answer: C. 8/19

Favourable = 8, total = 19. P = 8/19.

Q3. A bag contains 8 red, 9 blue and 5 green balls. One ball is drawn at random. What is the probability that it is green?

  1. 5/17
  2. 5/22
  3. 5/23
  4. 17/22
  5. 3/11
Show answer and solution

Answer: B. 5/22

Favourable = 5, total = 22. P = 5/22.

Q4. A bag contains 2 red, 2 blue and 4 green balls. One ball is drawn at random. What is the probability that it is red?

  1. 1/3
  2. 3/8
  3. 3/4
  4. 1/4
  5. 1/8
Show answer and solution

Answer: D. 1/4

Favourable = 2, total = 8. P = 1/4.

Q5. A bag contains 8 red, 8 blue and 1 green balls. One ball is drawn at random. What is the probability that it is green?

  1. 1/18
  2. 1/17
  3. 16/17
  4. 1/16
  5. 2/17
Show answer and solution

Answer: B. 1/17

Favourable = 1, total = 17. P = 1/17.

Q6. A bag contains 4 red, 9 blue and 6 green balls. One ball is drawn at random. What is the probability that it is green?

  1. 13/19
  2. 3/10
  3. 7/19
  4. 6/19
  5. 1/19
Show answer and solution

Answer: D. 6/19

Favourable = 6, total = 19. P = 6/19.

Q7. A bag contains 9 red, 8 blue and 7 green balls. One ball is drawn at random. What is the probability that it is red?

  1. 5/8
  2. 3/5
  3. 1/24
  4. 3/8
  5. 9/25
Show answer and solution

Answer: D. 3/8

Favourable = 9, total = 24. P = 3/8.

Q8. A bag contains 6 red, 2 blue and 1 green balls. One ball is drawn at random. What is the probability that it is green?

  1. 2/9
  2. 1/8
  3. 1/10
  4. 1/9
  5. 8/9
Show answer and solution

Answer: D. 1/9

Favourable = 1, total = 9. P = 1/9.

Q9. A box has 8 red, 8 green and 8 blue pens. Two pens are drawn at random. What is the probability that at least one is blue?

  1. 10/23
  2. 7/69
  3. 32/69
  4. 157/276
  5. 13/23
Show answer and solution

Answer: E. 13/23

P(no blue) = 16C2/24C2 = 10/23. P(at least one blue) = 1 − that = 13/23.

Q10. A bag has 7 red and 6 black balls. Two balls are drawn at random without replacement. What is the probability that both are red?

  1. 5/26
  2. 7/26
  3. 49/169
  4. 42/169
  5. 7/13
Show answer and solution

Answer: B. 7/26

P = 7C2 / 13C2 = 21/78 = 7/26.

Q11. A committee of 3 is to be chosen from 6 men and 7 women. What is the probability that it has exactly 3 women?

  1. 1
  2. 35/572
  3. 35/286
  4. 5/26
  5. 1/286
Show answer and solution

Answer: C. 35/286

Favourable = 7C3 × 6C0 = 35; total = 13C3 = 286. P = 35/286.

Q12. A committee of 3 is to be chosen from 7 men and 7 women. What is the probability that it has exactly 3 women?

  1. 1
  2. 5/104
  3. 5/52
  4. 1/364
  5. 5/26
Show answer and solution

Answer: C. 5/52

Favourable = 7C3 × 7C0 = 35; total = 14C3 = 364. P = 5/52.

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