E and F are mutually exclusive events. P(E) = 0.1; P(F) = 0.4. Find P(E|F). (Enter your answer to one decimal place.)P(E|F) =

Step 1: Break Down the Problem

We need to find the conditional probability $P(E|F)$ given two mutually exclusive events $E$ and $F$ with the following probabilities:

• $P(E) = 0.1$
• $P(F) = 0.4$

Step 2: Relevant Concepts

For mutually exclusive events, the occurrence of one event implies the non-occurrence of the other. Thus, the formula for conditional probability is: $P(E|F) = \frac{P(E \cap F)}{P(F)}$ However, since $E$ and $F$ are mutually exclusive, $P(E \cap F) = 0$.

Step 3: Analysis and Detail

Since $E$ and $F$ cannot happen at the same time: $P(E \cap F) = 0$ Now substituting this into the conditional probability formula: $P(E|F) = \frac{0}{P(F)} = \frac{0}{0.4} = 0$

Step 4: Verify and Summarize

The calculations show that due to the mutually exclusive nature of events $E$ and $F$, the probability of $E$ occurring given that $F$ has occurred is $0$.

Final Answer

$P(E|F) = 0.0$