Question 1

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, what is the probability that it is either red or green?

Accepted Answer

Step 1: Total number of balls = 5 + 3 + 2 = 10. Step 2: Number of red or green balls = 5 + 2 = 7. Step 3: Probability = Favourable outcomes / Total outcomes = 7/10 = 0.7. Therefore, the answer is 7/10.

Question 2

A student has a 60% chance of passing Mathematics and a 75% chance of passing English. Assuming the events are independent, what is the probability that the student passes at least one subject?

Accepted Answer

Step 1: P(pass Math) = 0.6, P(pass English) = 0.75. Step 2: P(at least one) = 1 - P(fail both). Step 3: P(fail Math) = 1 - 0.6 = 0.4. P(fail English) = 1 - 0.75 = 0.25. Step 4: P(fail both) = 0.4 × 0.25 = 0.1. Step 5: P(at least one) = 1 - 0.1 = 0.9 = 9/10.

Question 3

A bag contains 5 red balls, 7 blue balls, and 8 green balls. If two balls are drawn simultaneously at random, what is the probability that both balls are of the same colour?

Accepted Answer

Step 1: Total balls = 5 + 7 + 8 = 20. Total ways to draw 2 balls = C(20,2) = 190. Step 2: Ways to draw 2 red balls = C(5,2) = 10. Ways to draw 2 blue balls = C(7,2) = 21. Ways to draw 2 green balls = C(8,2) = 28. Step 3: Favourable outcomes = 10 + 21 + 28 = 59. Step 4: Probability = 59/190.

Question 4

A bag contains 5 red balls, 7 blue balls, and 8 green balls. Two balls are drawn simultaneously without replacement. What is the probability that both balls are of different colours?

Accepted Answer

Step 1: Total balls = 5 + 7 + 8 = 20. Total ways to draw 2 balls = C(20,2) = 190. Step 2: Ways to draw both same colour = C(5,2) + C(7,2) + C(8,2) = 10 + 21 + 28 = 59. Step 3: Ways to draw different colours = 190 - 59 = 131. Step 4: Probability = 131/190.

IBPS RRB PO Probability

Probability— Rules & Concept

Key Points to Remember

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Probability — Practice Questions

60-Second Revision — Probability