Posterior Probability of Gender Given Infection

A population is split evenly between men and women. A disease infects 3% of men but only 1% of women. You randomly select a person and discover they are infected. What is the probability that the infected person is male? Generalize: if the population has fraction $q$ male, men are infected at rate $p_M$, and women at rate $p_F$, derive $P(\text{Male} \mid \text{Infected})$.