SOLUTION: P(A) = 0.5, P(B) = 0.15, P(A | B) = 0.8 Use the appropriate laws of probability to calculate P(A ∪ B)

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Question 766570: P(A) = 0.5, P(B) = 0.15, P(A | B) = 0.8
Use the appropriate laws of probability to calculate P(A ∪ B)
Answer by Edwin McCravy(20054) About Me  (Show Source):
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P(A) = 0.5, P(B) = 0.15, P(A|B) = 0.8  Find P(A⋃B)

First we need this conditional probability law 

          P(A⋂B)
P(A|B) = 覧覧覧覧
           P(B)


          P(A⋂B)
   0.8 = 覧覧覧覧
           0.15

Multiply both sides by 0.15 to clear the fraction

(0.8)(0.15) = P(A⋂B)

       0.12 = P(A⋂B)

Now we need the equation for the union:

P(A⋃B) = P(A) + P(B) - P(A⋂B)
       = 0.5 + 0.15 - 0.12
       = 0.53

Edwin