Given that E and F are events such that
`P(E)=0.6,P(F)=0.3` and `P(E nn F)=0.2`.
then (i) `P(E//F)=(2)/(3)` (ii) `P(F//E)=(2)/(3)`.

Answer

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

**Given:**
- \( P(E) = 0.6 \)
- \( P(F) = 0.3 \)
- \( P(E \cap F) = 0.2 \)

**Step 1: Calculate \( P(E|F) \)**

The formula for conditional probability is:
\[ P(E|F) = \frac{P(E \cap F)}{P(F)} \]

Substituting the known values:
\[ P(E|F) = \frac{P(E \cap F)}{P(F)} = \frac{0.2}{0.3} \]

Calculating this gives:
\[ P(E|F) = \frac{2}{3} \]

**Step 2: Calculate \( P(F|E) \)**

Using the same formula for conditional probability:
\[ P(F|E) = \frac{P(E \cap F)}{P(E)} \]

Substituting the known values:
\[ P(F|E) = \frac{P(E \cap F)}{P(E)} = \frac{0.2}{0.6} \]

Calculating this gives:
\[ P(F|E) = \frac{1}{3} \]

**Conclusion:**
- \( P(E|F) = \frac{2}{3} \) (True)
- \( P(F|E) = \frac{1}{3} \) (False)

Thus, the first statement \( P(E|F) = \frac{2}{3} \) is true, and the second statement \( P(F|E) = \frac{2}{3} \) is false.