Suppose that P(A|B)=0.3, P(B|A)=0.1 and P(AB)=0.03. What is P(A)?

The formula for conditional probability is P(A|B) = P(AB) / P(B).

We know that P(A|B) = 0.3 and P(AB) = 0.03. We can substitute these values into the formula to find P(B):

0.3 = 0.03 / P(B)

Solving for P(B), we get P(B) = 0.03 / 0.3 = 0.1.

Next, we use the formula for conditional probability again, but this time to find P(A). We know that P(B|A) = 0.1 and we just found that P(B) = 0.1. Substituting these values into the formula, we get:

0.1 = P(AB) / P(A)

Substituting the known value of P(AB) = 0.03, we get:

0.1 = 0.03 / P(A)

Solving for P(A), we get P(A) = 0.03 / 0.1 = 0.3.

So, P(A) = 0.3.