A bag contains 8 red and 5 white balls (13 total). Two balls are drawn without replacement. What is the probability that both balls drawn are white?

Introduction / Context:
For draws without replacement, probabilities change after each draw. The exact probability that both draws are white can be computed by sequential multiplication or combinatorics.

Given Data / Assumptions:

• Red = 8, White = 5, Total = 13.
• Two draws without replacement.

Concept / Approach:
Method 1 (sequential): P(white first) * P(white second | white first). Method 2 (combinatorial): C(5,2) / C(13,2).

Step-by-Step Solution (combinatorial):
Favourable ways = C(5,2) = 10.Total ways = C(13,2) = 78.Probability = 10/78 = 5/39.

Verification / Alternative check (sequential):
P = (5/13) * (4/12) = 20/156 = 5/39, same result.

Why Other Options Are Wrong:
5/16 assumes replacement or independence; 2/13 and 3/26 do not match either correct computation.

Common Pitfalls:
Treating draws as independent when they are without replacement; forgetting to reduce the denominator after the first draw.

Final Answer:
5/39