1. **State the problem:** We are given the probability that Nathan buys butter, $P(B) = 0.10$, and the probability that he buys both bread and butter, $P(A \cap B) = 0.20$. We need to find the probability that he buys butter given that he already bought bread, which is $P(B|A)$. 2. **Recall the formula for conditional probability:** $$ P(B|A) = \frac{P(A \cap B)}{P(A)} $$ This formula tells us how to find the probability of event $B$ occurring given that event $A$ has occurred. 3. **Identify what is known and unknown:** - $P(B) = 0.10$ - $P(A \cap B) = 0.20$ - $P(A)$ is unknown and needed to find $P(B|A)$. 4. **Check for consistency:** Since $P(A \cap B) \leq P(B)$ and $P(A \cap B) \leq P(A)$, but here $P(A \cap B) = 0.20$ is greater than $P(B) = 0.10$, this is impossible under normal probability rules. The joint probability cannot be greater than the probability of one of the events. 5. **Conclusion:** The given probabilities are inconsistent, so the problem as stated cannot be solved with these values. Please verify the probabilities provided. **Final answer:** The problem data is inconsistent; $P(A \cap B)$ cannot be greater than $P(B)$.