SOLUTION: P(A) = 0.25 and P(A ∪ B) = 0.6 find P(B) , for independent event

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Question 1048511: P(A) = 0.25 and P(A ∪ B) = 0.6 find P(B) , for independent event
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

P(A) = 0.25 and P(A ∪ B) = 0.6 find P(B)

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

For independent events P(A ∩ B) = P(A)∙P(B)

P(A ∪ B) = P(A) + P(B) - P(A)∙P(B)

     0.6 = 0.25 + P(B) - 0.25∙P(B)

Remove the decimals by multiplying through by 100

      60 = 25 + 100∙P(B) - 25∙P(B)
     
      60 = 25 + 75∙P(B)

      35 = 75∙P(B)

     

           

Edwin
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