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Chapter 9: Problem 72

Determine whether the statement is true or false. Justify your answer. If \(A\) and \(B\) are independent events with nonzero probabilities, then \(A\) can occur when \(B\) occurs.

Short Answer

Expert verified
The statement is true. If \(A\) and \(B\) are independent events, then \(A\) can occur when \(B\) occurs because the occurrence of one event does not affect the occurrence of the other.

Step by step solution

01

Understanding Independence

Two events are said to be independent if the occurrence of one event does not influence the occurrence of the other. In terms of probability, this can be written as \(P(A \cap B) = P(A) \cdot P(B)\), where \(A\) and \(B\) are two independent events.
02

Application on Given Problem

Given \(A\) and \(B\) are independent events with nonzero probabilities, it means that the occurrence of \(A\) does not affect the occurrence of \(B\) and vice versa.
03

Decision on the Statement

Therefore, \(A\) can occur when \(B\) occurs because the occurrence of \(B\) does not affect the occurrence of \(A\). Hence, the original statement is true.

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