P(correct guess) = P(we were shown the higher number H) * P(we guessed "high" given H) + P(we were shown the lower number L) * P(we guessed "low" given L) => (plugging in from the original selection method) P(correct guess) = (1/2) * (1 - F(H)) + (1/2) * F(L) => P(correct guess) = (1/2) (1 - (F(H) - F(L))) => Since F(H) - F(L) > 0 (by assumption) P(correct guess) = (1/2) (1 - (a positive value)) => Therefore, P(correct guess) < 1/2.