91Ó°ÊÓ

Since E and F are mutually exclusive events, that means they cannot both occur at the same time, and their intersection is EMPTY. In other words, \(E \cap F = \emptyset\). So, when determining the conditional probability of E given F, we know that it is impossible for both events to occur simultaneously. The formula for conditional probability is: \(P(E|F) = \dfrac{P(E \cap F)}{P(F)}\) However, since E and F are mutually exclusive, \(P(E \cap F) = 0\). Therefore: \(P(E|F) = \dfrac{0}{P(F)} = 0\)

Since E is a subset of F, this means that every time event E occurs, event F also occurs. In this case, we can use the formula for conditional probability: \(P(E|F) = \dfrac{P(E \cap F)}{P(F)}\) But, since E is a subset of F, E ∩ F = E. As a result, the probability of their intersection is equal to the probability of E: \(P(E \cap F) = P(E) = 0.6\) Now, we need to divide this by the probability of F. Since \(E \subseteq F\), it follows that \(P(E) \leq P(F)\), i.e., the probability of F must be greater than or equal to the probability of E. Therefore, \(0.6 \leq P(F) \leq 1\) Finally, we can write the conditional probability as: \(P(E|F) = \dfrac{P(E)}{P(F)} = \dfrac{0.6}{P(F)}\) Since we don't have the exact value of \(P(F)\), we can only say that \(\dfrac{0.6}{1} \leq P(E|F) \leq \dfrac{0.6}{0.6}\) That is, \(0.6 \leq P(E|F) \leq 1\)

In this case, event F is a subset of event E. It means that every time event F occurs, event E also occurs. We can use the conditional probability formula again: \(P(E|F) = \dfrac{P(E \cap F)}{P(F)}\) Since F is a subset of E, E ∩ F = F. As a result, the probability of their intersection is equal to the probability of F: \(P(E \cap F) = P(F)\) Finally, we can write the conditional probability as: \(P(E|F) = \dfrac{P(E \cap F)}{P(F)} = \dfrac{P(F)}{P(F)} = 1\) So in this case, \(P(E|F) = 1\).