SOLUTION: P(A)=0.39 P(B)=0.35 A and B are dependent. P(A∣B)=0.385 Find P(A∩B) Find P(A∪B) Find P(B∣A)

Question 1151979: P(A)=0.39
P(B)=0.35
A and B are dependent.
P(A∣B)=0.385
Find P(A∩B)
Find P(A∪B)
Find P(B∣A)
Answer by ikleyn(52877) (Show Source): You can put this solution on YOUR website!
.


P(A | B)  actually means and is the same as  P(A ∩ B)/P(B).


Therefore, the given  P(A | B) = 0.3855  means that  P(A ∩ B)/P(B) = 0.385.


Multiplying both sides of the last equality by P(B), you get


    P(A ∩ B) = 0.385*P(B) = 0.385*0.35 = 0.13475.


To find P(A U B), use the general formula


    P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.39 + 0.35 - 0.13475 = 0.60525.    


Last step,   P(B|A) = P(B ∩ A) / P(A) = P(A ∩ B) / P(A) =  = 0.345513.

Solved.   I answered all questions.

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