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Chapter 11: Problem 76

What does \(P(B \mid A)\) mean? Give an example.

Short Answer

Expert verified
The notation \(P(B \mid A)\) represents the probability of event B occurring, given that event A has already occurred. For instance, consider the events 'it is raining (A)' and 'carrying an umbrella (B)'. Here, \(P(B \mid A)\) would denote the probability of a person carrying an umbrella given that it is raining, which would generally be higher than on a non-rainy day.

Step by step solution

01

Understanding Conditional Probability

Conditional probability, denoted as \(P(B \mid A)\), refers to the probability of an event B occurring, assuming that another event A has already occurred.
02

Example of Conditional Probability

For example, consider the event \(A\) to be 'it is raining', and event \(B\) to be 'carrying an umbrella'. \(P(B \mid A)\) here would represent the probability that someone is carrying an umbrella given that it is raining. In reality, this probability would be significantly higher than the probability of someone carrying an umbrella on a non-rainy day.

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