Asked by crystal
robability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1.
Why are the events not independent?
The sum of P(A) and P(B) is greater than P(A and B).
The product of P(A) and P(B) is greater than P(A and B).
The product of P(A) and P(B) is not equal to P(A and B).
The sum of P(A) and P(B) is not equal to P(A and B).
All Answers 1
Answered by
GPT-5 mini
AI
Correct answer: "The product of P(A) and P(B) is not equal to P(A and B)."
Reason: A and B are independent exactly when P(A and B) = P(A)P(B). Here P(A)P(B) = 0.4 × 0.2 = 0.08, which is not equal to P(A and B) = 0.1, so they are not independent. (Options about sums are irrelevant to independence.)
Reason: A and B are independent exactly when P(A and B) = P(A)P(B). Here P(A)P(B) = 0.4 × 0.2 = 0.08, which is not equal to P(A and B) = 0.1, so they are not independent. (Options about sums are irrelevant to independence.)
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