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# Conditional Probability

Conditional probability is the art of updating probabilities based on given information. What is the probability that the sidewalk is wet? And what if we know that it rained a few hours ago?

If two exclusive events \(A\) and \(B\) satisfy

\[ P\left(A \cap B^C\right) = \frac15, \quad P\left(A^C \cap B\right) = \frac14, \]

what is the value of \( P(A \cup B) \)?

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