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Thread: independant events, probability

  1. #1
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    independant events, probability

    Events A and B are independent.
    Given also that
    P(A) = 3/4 and P(A ∩ B ′ ) = 1/4

    Find
    (a) P(A ∩ B),
    (b) P(B),
    (c) P(A′ ∩ B ′ ).
    can someone please explain in this question If events and A and B are independent of each other, than why is it that the p (A ∩ B ′) = 1/4?
    Is that not the probability that event 'A' happens and 'B' does not , should it not also equal 3/4 ? As my understanding is if both events are independent of each other than the probability of 'A' happening is the same weather or not 'B' has happened.



    Thanks.
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  2. #2
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    If events E~\&~F are independent then that tell you P(E \cap F) = P(E)P(F).
    Each of these pairs is independent: E~\&~{F'}, {E'}~\&~F, {E'}~\&~{F'}.

    So you know that \frac{1}{4} = P(A \cap B') = P(A)P(B').
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