Explanation

This is a conditional probability problem. We are asked to find P(B|A) - the probability that Yena's ROE exceeds 30% given that Xela's ROE has already exceeded 20%.

Given:

• P(A) = Probability that Xela's ROE > 20% = 0.10
• P(B) = Probability that Yena's ROE > 30% = 0.05
• P(A ∩ B) = Probability that both events occur = 0.02

Using the conditional probability formula: $P(B|A) = \frac{P(A \cap B)}{P(A)}$

Calculation: $P(B|A) = \frac{0.02}{0.10} = 0.20$

Interpretation:

• The result 0.20 means that if we know Xela's ROE has exceeded 20%, there's a 20% chance that Yena's ROE will also exceed 30%.
• This is higher than the unconditional probability of Yena's ROE exceeding 30% (which is 0.05), suggesting some positive correlation between the performance of the parent company and its subsidiary.

Why other options are incorrect:

• B (0.1): This is simply P(A) = 0.10, not the conditional probability.
• C (0.05): This is P(B) = 0.05, the unconditional probability of Yena's ROE exceeding 30%.
• D (0.025): This would be P(A) × P(B) = 0.10 × 0.05 = 0.005 if the events were independent, but the actual joint probability is higher (0.02), indicating dependence.