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Math Help - Probability

  1. #1
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    Probability

    Consider two events: E and F. P(E)=P(F)=.7
    Suppose we know that P(F|E)=.9. What is the probability that at least one of them occurs?

    I know that the answer is .77 (I have the key) but I don't know how to do it and I can't find anything in my notes to help me out. Thanks.
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  2. #2
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    Hello, Paschendale!

    Consider two events: E\text{ and }F, where P(E)\:=\:P(F)\:=\:0.7

    Suppose we know that: P(F|E)\:=\:0.9

    What is the probability that at least one of them occurs?

    Your notes must include Bayes' Theorem: . P(F|E) \;=\;\frac{P(F \cap E)}{P(E)}

    So we have: . P(F|E) \;=\;\frac{P(F \cap E)}{0.7} \;=\;0.9 \quad\Rightarrow\quad P(F \cap E) \;=\;0.63


    Then: . P(F \cup E) \;=\;P(F) + P(E) - P(F \cap E)

    . . . . . . . . . . . . = \;\;\;0.7 \;\;+\;\; 0.7 \;\;-\;\; 0.63

    . . . . . . . . . . . . =\;\;\;0.77

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  3. #3
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    Ok I think I get it. Thanks dude.
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