Determine event independence using P(A and B)=P(A)P(B).
Decide whether two events are independent by comparing P(A and B) to P(A)P(B)
Problem
Interpret this independence test result in context: a survey shows \(P(A~\text{and}~B)=P(A)P(B)\) for grade level and club membership.
Big Picture
What this problem is really about
The reported joint-equals-product equation is exactly the probability criterion for independence. We’ll define the two contextual events, match the equality to that criterion, translate the classification into a statement about unchanged modeled probability, and avoid confusing independence with impossibility or certainty.
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