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

Answer:

P(A) = 0.575 = 23/40

Step-by-step explanation:

The definition of Conditional Probability says $P(B|A)=\frac{P(A\cap B)}{P(A)}$.  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).

$0.8 = \frac{0.46}{P(A)}\\\\0.8 \cdot P(A) = 0.46\\\\P(A) = \frac{0.46}{0.8} = 0.575$