Let P be a probability function on = {a, b} such that P(a) = p and P(b) = 1 p for 0

Let P be a probability function on Ω = {a, b} such that P(a) = p and P(b) = 1 − p for 0 ≤ p ≤ 1. Let Q be a function on Ω defined by Q(ω) = [P(ω)]². For what value(s) of p will Q be a valid probability function?