If E and F are two events associated with the same sample space of a random experiment then P(E|F) is given by __________

P(E|F) is given by the formula:

P(E|F) = P(E ∩ F) / P(F)

This is known as the conditional probability of E given F.

Here's a step by step breakdown:

1. P(E|F) is the probability of event E happening given that event F has already happened.

2. P(E ∩ F) is the probability of both events E and F happening.

3. P(F) is the probability of event F happening.

4. To find P(E|F), you divide the probability of both events happening by the probability of event F.

This formula is used when the outcome of one event affects the outcome of another. For example, the probability of it raining today (event E) given that it is cloudy (event F).