Example

• W : The event that the conversation was held with a woman
• L : The event that the conversation was held with a long-haired person
• P(W) = 0.5
• P(L|W) = 0.75 (Suppose it is known that 75% of women have long hair)
• P(L|M) = 0.15 (Suppose it is known that 15% of men have long hair)

P(W|L) &= \frac{P(L|W)\, P(W)}{P(L)} \\ &= \frac{P(L|W)\, P(W)}{P(L|W)\, P(W) + P(L|M)\, P(M)} \\ &= \frac{0.75\cdot0.50}{0.75\cdot0.50 + 0.15\cdot0.50} \\ &= \frac56 \\ &\approx 0.83