Question 1160923
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Note that the complement to  (A U B')  is  (A' &#8745; B).

Therefore, P(A' &#8745; B) = 1 - P(A U B') = 1 - 0.8 = 0.2.



Next,        (A' &#8745; B) U  (A &#8745; B) = B,  and the sets  (A' &#8745; B) and  (A &#8745; B)  are disjoint.

Therefore,  P(A' &#8745; B) + P(A &#8745; B) = P(B),   or

              0.2     + P(A &#8745; B) = 0.5,


which implies  P(A &#8745; B) = 0.5 - 0.2 = 0.3.



Hence, by the definition of the <U>conditional probability</U>, 

           P(A | B) = P(A &#8745; B) / P(B) = {{{0.3/0.5}}} = 0.6.    <U>ANSWER</U>
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Solved.