Question

A bag contains 3 red and 5 black balls. Two balls are drawn at random. What is the probability that both are red?

• A. $\frac{3}{28}$
• B. $\frac{3}{56}$
• C. $\frac{1}{14}$
• D. $\frac{1}{28}$

Hint:

Use combinations or sequential probability for drawing without replacement.

Answer 1

The Correct Option is A

- Step 1: Total balls = $3 + 5 = 8$. Total ways to draw 2 balls = $\binom{8}{2} = \frac{8 \times 7}{2} = 28$.
- Step 2: Ways to draw 2 red balls = $\binom{3}{2} = 3$.
- Step 3: Probability = $\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{3}{28}$.
- Step 4: Verify: Alternative method: Probability of first red = $\frac{3}{8}$, second red = $\frac{2}{7}$, so $\frac{3}{8} \times \frac{2}{7} = \frac{6}{56} = \frac{3}{28}$.
- Step 5: Option (1) matches.