Determine event independence using P(A and B)=P(A)P(B).
Test two events for independence using joint and marginal probabilities
Problem
Test whether getting heads on a fair coin and rolling a \(4\) on a fair die are independent by comparing their joint probability \(1/12\) with \((1/2)(1/6)\).
Big Picture
What this problem is really about
Separate random devices suggest independence, but the probability equation provides the proof. We’ll define the coin and die events, record their marginals and joint probability, multiply the marginals, and interpret exact equality as neither result changing the other event’s probability.
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