Question

There are two urns. One contains two white balls and four red balls, the other contains three white and nine red balls. All balls are of the same shape and size. From each urn, one ball is drawn. What is the probability of getting both the balls of the same colour?

• A. 7/12
• B. 1/2
• C. 1/24
• D. 1/12

Hint:

When solving probability questions involving “same colour” or “same type”, split into mutually exclusive cases and add their probabilities.

Answer 1

The Correct Option is A

We have two favourable cases: Case 1 — Both balls are white.
Probability from Urn 1 (white) = \( \frac{2}{6} = \frac{1}{3} \).
Probability from Urn 2 (white) = \( \frac{3}{12} = \frac{1}{4} \).
Combined probability = \( \frac{1}{3} \times \frac{1}{4} = \frac{1}{12} \).
Case 2 — Both balls are red.
Probability from Urn 1 (red) = \( \frac{4}{6} = \frac{2}{3} \).
Probability from Urn 2 (red) = \( \frac{9}{12} = \frac{3}{4} \).
Combined probability = \( \frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2} \).
Total probability = \( \frac{1}{12} + \frac{1}{2} = \frac{1}{12} + \frac{6}{12} = \frac{7}{12} \).