Question

Events A and B are dependent. Suppose P(B|A)=0.8 and P(A and B)=0.46. Find P(A).

Answer 1

P(A) = 0.575 = 23/40

Explanation:

The definition of Conditional Probability says
`P(B|A)=(P(A\cap B))/(P(A))`. The question gives specific number values for two of those three quantities, so plug in the given numbers and solve for the unknown P(A).

`0.8 = (0.46)/(P(A))\\\\0.8 \cdot P(A) = 0.46\\\\P(A) = (0.46)/(0.8) = 0.575`