# Let A1, A2 and A3 be mutually exclusive and exhaustive events of some sample space S, where P(A1) = P(A2) = 0.3. Suppose that 1 10 of A1 observations support the Standard Model, 1 2 of A2 observations support the Standard Model, and 2 5 of A3 observations support the Standard Model. Given that an observation does not support the Standard Model, calculate the probability that it is classified in A3.

Question

Let A1, A2 and A3 be mutually exclusive and exhaustive events of some sample space S, where P(A1) = P(A2) = 0.3. Suppose that 1 10 of A1 observations support the Standard Model, 1 2 of A2 observations support the Standard Model, and 2 5 of A3 observations support the Standard Model. Given that an observation does not support the Standard Model, calculate the probability that it is classified in A3.