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4 June, 03:49

Which statement is true about whether A and B are independent events? A and B are independent events because P (A∣B) = P (A) = 0.12. A and B are independent events because P (A∣B) = P (A) = 0.25. A and B are not independent events because P (A∣B) = 0.12 and P (A) = 0.25. A and B are not independent events because P (A∣B) = 0.375 and P (A) = 0.25

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  1. 4 June, 03:56
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    The events A and B are independent if the probability that event A occurs does not affect the probability that event B occurs.

    A and B are independent if the equation P (A∩B) = P (A) P (B) holds true.

    P (A∩B) is the probability that both event A and B occur.

    Conditional probability is the probability of an event given that some other event first occurs.

    P (B|A) = P (A∩B) / P (A)

    In the case where events A and B are independent the conditional probability of event B given event A is simply the probability of event B, that is P (B).

    Statement 1:A and B are independent events because P (A∣B) = P (A) = 0.12. This is true.

    Statement 2: A and B are independent events because P (A∣B) = P (A) = 0.25.

    This is true.

    Statement 3: A and B are not independent events because P (A∣B) = 0.12 and P (A) = 0.25.

    This is true.

    Statement 4: A and B are not independent events because P (A∣B) = 0.375 and P (A) = 0.25

    This is true.
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