Answer to Question #330923 in Statistics and Probability for levia

Question

If P(B) = 0.15, P(A | B) = 0.50, P(B′) = 0.85, and P(A | B′) = 0.60, find P(B | A)

Answer 1

$P(B|A) =\cfrac{P(B)\cdot P(A|B) } {P(B)\cdot P(A|B)+P( B')\cdot P(A|B')} =\\ =\cfrac{0.15\cdot0.50} {0.15\cdot0.50+0.85\cdot0.60} =\\0.1282.$