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Chapter 4: Problem 31

Briefly explain the meaning of independent and dependent events. Suppose \(A\) and \(B\) are two events. What formula will you use to prove whether \(A\) and \(B\) are independent or dependent?

Short Answer

Expert verified
Independent events are those where occurrence of one event doesn't affect the occurrence of the other. Dependent events are opposite, an event's result impacts the probability of another event's result. To check if events are independent or dependent, use the formula \(P(A 鈭� B) = P(A) * P(B)\). If the equality is valid, they're independent, otherwise they're dependent.

Step by step solution

01

Definition of Independent Events

Two events \(A\) and \(B\) are said to be independent if the occurrence of \(A\) does not affect the occurrence of \(B\), and vice versa. That is, the probability of \(B\) taking place if \(A\) has already occured is the same as the probability of \(B\) taking place anyway.
02

Definition of Dependent Events

Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second, so that the probabilities are not the same. In simple terms, the probability of Event \(B\) depends on Event \(A\).
03

Formula to Verify Dependence or Independence

The formula used to determine if two events are independent is \(P(A 鈭� B) = P(A) * P(B)\). If this equality holds true, the events \(A\) and \(B\) are independent. If it doesn't, the events are dependent.

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