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Math Help - Quick Probability Questions

  1. #1
    Junior Member
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    Quick Probability Questions

    1) A and B are two independent events such that P(A)=alpha and P(A union B)= beta, Beta>Alpha. Show that:

    P(B)= Beta-Alpha/ 1-Alpha

    2) Given that P(E)=1/3, P(F)=1/2, P (E' intersection F)=1/2, find the value of P (E' intersection F').

    Thanks in advance
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  2. #2
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    \begin{array}{rcl}<br />
 \beta  & = & P(A \cup B) \\ <br />
  & = & P(A) + P(B) - P(A)P(B)\;\left[ \mbox{Independent} \right] \\ <br />
  & = & \alpha  + P(B) - \alpha P(B) \\ <br />
 \end{array}

    Now solve for P(B).
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