What is the conditional probability of event A given P(A and B) = 0.2 and P(B) = 0.5?

The conditional probability of event A given P(A and B) = 0.2 and P(B) = 0.5 is 0.4.

To find the conditional probability of event A given event B, we use the formula: P(A|B) = P(A and B) / P(B). This formula tells us how likely event A is to happen if we already know that event B has occurred.

In this case, we are given that P(A and B) = 0.2 and P(B) = 0.5. Plugging these values into the formula, we get:

P(A|B) = P(A and B) / P(B) = 0.2 / 0.5 = 0.4.

This means that if event B has occurred, the probability that event A will also occur is 0.4, or 40%.

Understanding conditional probability is important because it helps us analyse situations where events are dependent on each other. For example, if you know it is raining (event B), you might be more likely to carry an umbrella (event A). By using the given probabilities, we can make more informed predictions about such scenarios.