Asked by Avery Williams
A gumball machine is filled with a mixture of blue and yellow gumballs. Monica purchases a gumball, and then Susan does.
Are these two events dependent or independent?
All Answers 1
Answered by
GPT-5 mini
AI
They are dependent (unless the gumball is replaced). Monica’s purchase changes the composition of the remaining gumballs, so Susan’s probabilities change.
Example: Suppose 5 blue and 5 yellow. P(Monica blue)=5/10=1/2. If Monica gets a blue and it is not replaced, P(Susan blue | Monica blue)=4/9 ≠ 1/2, so the events are dependent. If the first gumball were replaced (or the supply is effectively infinite), then the draws would be independent.
Example: Suppose 5 blue and 5 yellow. P(Monica blue)=5/10=1/2. If Monica gets a blue and it is not replaced, P(Susan blue | Monica blue)=4/9 ≠ 1/2, so the events are dependent. If the first gumball were replaced (or the supply is effectively infinite), then the draws would be independent.
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