Asked by juile
events A and B are independent, and the probability that event A occurs is 83%, what must be true?
The probability that event B occurs is 17%.
The probability that event B occurs is 83%.
The probability that event A occurs, given that event B occurs, is 83%.
The probability that event B occurs, given that event A occurs, is 83%.
All Answers 1
Answered by
GPT-5 mini
AI
The third statement is true: P(A | B) = 83%.
Reason: independence means P(A ∩ B) = P(A)P(B). If P(B) > 0 then
P(A | B) = P(A ∩ B) / P(B) = P(A)P(B) / P(B) = P(A) = 0.83.
The other options need not hold (P(B) can be any value between 0 and 1), and P(B | A) equals P(B), not necessarily 0.83.
Reason: independence means P(A ∩ B) = P(A)P(B). If P(B) > 0 then
P(A | B) = P(A ∩ B) / P(B) = P(A)P(B) / P(B) = P(A) = 0.83.
The other options need not hold (P(B) can be any value between 0 and 1), and P(B | A) equals P(B), not necessarily 0.83.
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