Fun with Bayes' Theorem.

5% of Republican Congressmen are closeted gay men. 90% of closeted gay Republican Congressmen are publicly homophobic. 50% of heterosexual Republican Congressmen are also homophobic. A Republican Congressman has just announced that he thinks homosexuals are an abomination and that the Lord’s punishment on them will be swift and just. What is the probability that he is actually visiting truck stop bathrooms when he tells his wife he’s at campaign meetings?

P(gay | homophobic) (the PROBABILITY that the man is gay GIVEN THE FACT that he is homophobic)

= P(homophobic | gay)*P(gay) / (P(homophobic | gay)*P(gay) + P(homophobic | ~gay)*P(~gay))

= 90%*5% / (90%*5% + 50%*95%)

= 4.5% / (4.5% + 47.5%)

~ 8.65%