Applications of Probability — Test

Question 3 • Geometry

The events "male” and "buys lunch” are not independent because

Answer

cap p times open paren buys lunch divides male close paren is equal to 0 point 3 and cap p times male is equal to 0 point 4 .

cap p times open paren male divides buys lunch close paren is equal to 0 point 4 and cap p times male is equal to 0 point 3 .

cap p times open paren male divides buys lunch close paren is equal to cap p times male is equal to 0 point 3 .

cap p times open paren buys lunch divides male close paren is equal to cap p times male is equal to 0 point 4 .

Explanation

For two events to be independent, the probability of being male should be unchanged when we know someone buys lunch: P(male | buys lunch) = P(male). Choice A gives 0.4 and 0.3, which are different, so the events are not independent. The other choices either compare probabilities that do not test independence or state an equality that does not show a difference.

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