In an epidemic, the probability of having S|D is 0.2 and P(D) = 0.1. P(S|D') = 0.04 and P (D') = 0.01. What is the P(D|S)?

Answer 1

P(D|S) = P(S|D) * P(D) / P(S)

P(S) = P(S|D) * P(D) + P(S|D') * P(D')

P(D|S) = (0.2 * 0.1) / (0.2 * 0.1 + 0.04 * 0.01)

P(D|S) = 0.83