SOLUTION: Give that A and B are independent and P(A)=1/5 and P(AUB)=1/4. Find P(A') and P(B)

Question 1206354: Give that A and B are independent and P(A)=1/5 and P(AUB)=1/4. Find P(A') and P(B)
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Given that A and B are independent and P(A)=1/5 and P(AUB)=1/4. Find
(a) P(A')
(b) P(B)
~~~~~~~~~~~~~~~~~~~~~~~~~

(a)  P(A') = 1 - P(A) = 1 - 1/5 = 4/5.     (A' is the complement to B).



(b)  Use the general formula, which is always valid

         P(A U B) = P(A) + P(B) - P(A and B).    (1)


     Since A and B are independent, we have P(A and B) = P(A)*P(B) = .


     Substituting the values into formula (1), we get

          =  + P(B) - .


      Multiply both sides by 20

         5 = 4 + 20*P(B) - 4*P(B)

         5 - 4 = 16*P(B)

           1   = 16*P(B)

           P(B) = .   ANSWER

Solved.

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