If `P(E)=0.6,P(F)=0.3` and `P(E nn F)=0.2`, then find `P(E//F)`.

Answer

To find \( P(E|F) \), we can use the formula for conditional probability:

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

Where:
- \( P(E|F) \) is the probability of event \( E \) given that event \( F \) has occurred.
- \( P(E \cap F) \) is the probability of both events \( E \) and \( F \) occurring.
- \( P(F) \) is the probability of event \( F \).

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

Now, we can substitute the known values into the formula:

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

Now, we can simplify this fraction:

\[ P(E|F) = \frac{2}{3} \approx 0.6667 \]

Thus, the final answer is:

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