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Math Help - Independent events

  1. #1
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    Unhappy Independent events

    Hi there could anyone help me?

    True/false
    1) If events A and B are independent, then P (A & B) = P(A)P(B)
    2) It is possible for two independent events with positive probabilities to be mutually exclusive

    Thanks!
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by iamterribleatmaths View Post
    Hi there could anyone help me?

    True/false
    1) If events A and B are independent, then P (A & B) = P(A)P(B)
    2) It is possible for two independent events with positive probabilities to be mutually exclusive

    Thanks!
    1) T
    2) F

    The second is false because of the first property. Mutually exclusive means P(A \cap B) = 0, but if two events are independent, then P(A \cap B) = P(A)*P(B), so if both probabilities are non-zero, then the events are not mutually exclusive.
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  3. #3
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    Quote Originally Posted by iamterribleatmaths View Post
    Hi there could anyone help me?

    True/false
    1) If events A and B are independent, then P (A & B) = P(A)P(B) Mr F says: True by definition, as your textbook and/or notes would surely say.

    2) It is possible for two independent events with positive probabilities to be mutually exclusive Mr F says: False. By definition, Pr(A & B) = 0 if A and B are mutually exclusive events. But if A and B are independent events with positive probabilities, Pr(A & B) = Pr(A) Pr(B) neq 0 ....

    Thanks!
    ..
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