Question

For two events, A and B, P(A=0.2, P(B)=0.50, and P(A|B)=0.2.

a. Find P(A∩B) .b. Find P(B|A). (Simplify your answer)

b. P(B|A)=__________(Simplify your answer.)

Answer 1

Given that, P(A) = 0.2, P(B) = 0.50 and P(A | B) = 0.2

we want to find, the following probabilities,

a) We know,

$P(A | B) = \frac { P(A \cap B) }{P(B)}$

$P(A \cap B) = P(A|B) * P(B)$

$P(A \cap B) = 0.2*0.50$

$=>P(A \cap B) = 0.1$

b)

$P(B|A) = \frac {P(A \cap B) }{P(A)}$

$P(B|A) = \frac {0.1 }{0.2}$

$P(B|A) = 0.5$