Given that E and F are events such that
`P(E)=0.6,P(F)=0.3,P(E nn F)=0.2`.
Find P(E/F) and P(F/E).

Answer

To solve the problem, we need to find \( P(E|F) \) and \( P(F|E) \) using the given probabilities.

### Step 1: Find \( P(E|F) \)

We use the formula for conditional probability:

\[ P(E|F) = \frac{P(E \cap F)}{P(F)} \]

From the problem, we know:

- \( P(E \cap F) = 0.2 \)
- \( P(F) = 0.3 \)

Substituting these values into the formula:

\[ P(E|F) = \frac{0.2}{0.3} = \frac{2}{3} \]

### Step 2: Find \( P(F|E) \)

We again use the formula for conditional probability:

\[ P(F|E) = \frac{P(F \cap E)}{P(E)} \]

Since \( P(F \cap E) = P(E \cap F) \), we can use the same value:

- \( P(E \cap F) = 0.2 \)
- \( P(E) = 0.6 \)

Substituting these values into the formula:

\[ P(F|E) = \frac{0.2}{0.6} = \frac{1}{3} \]

### Final Answers:

- \( P(E|F) = \frac{2}{3} \)
- \( P(F|E) = \frac{1}{3} \)

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