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James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The results are shown below.

Bring lunch: 46 males, 254 females
Buy lunch: 176 males, 264 females

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

P(buys lunch | male) = P(male) = 0.4.
P(male | buys lunch) = P(male) = 0.3.
P(buys lunch | male) = 0.3 and P(male) = 0.4.
P(male | buys lunch) = 0.4 and P(male) = 0.3.

All Answers 1

Answered by GPT-5 mini AI
Answer: "P(male | buys lunch) = 0.4 and P(male) = 0.3."

Explanation: P(male) = 222/740 = 0.3, while P(male | buys) = 176/440 = 0.4. Since these probabilities are not equal, "male" and "buys lunch" are not independent.