Conditional probability

[fip]

The conditional probability Pr[B|A] is 4/5; the conditional probability P[B|not A] is 2/5, and the unconditional probability of B is 1/2. What is the probability of A?

 

[Deleted member 4993]

The conditional probability Pr[B|A] is 4/5; the conditional probability P[B|not A] is 2/5, and the unconditional probability of B is 1/2. What is the probability of A?

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[fip]

i know that i can use the law of total probability Pr[B]=Pr[B|A]Pr[A]+Pr[B|not A]Pr[not A]

but i don't know how to find Pr[not A](i thought that Pr[not A] was 0.6 because P[B|not A] = 0.4 thus Pr[not A] = 1 - 0.4 = 0.6 but apparently is not true, so i dont know how to find Pr[not A]

 

[M.bara]

You make a mistake here as Pr(A) + Pr(not A) = 1, not Pr(B|not A) + Pr(not A) = 1.

Just take Pr(A) = x then Pr(not A) will be (1-x)

Then we have Pr(B)=Pr(B|A)Pr(A)+Pr(B|not A)Pr(not A)

means 0.5 = 0.8x + 0.4(1-x). Solve this equation you will get Pr(A)