The Gay Left Handed Bayesian

Don't know why this little story problem jumped in my head, but here you go.

The number of people who are homosexual seems to be around 4.5% of the population (wikipedia says 2 to 7%). The percent of people who are left handed is about 10%. For males, being gay increases your chance of being left handed by 36% (90% for females) [link]. So if you meet a left handed man or woman, what are the chances they are homosexual?

Pulling out my book of Bayesian spells....

P(h) = 0.045 # probability of being homosexual
P(l) = 0.1 # probability of being left handed
P(l|h) = 0.1 * 1.36 = 0.136 for guys (or 0.19 for dames)# probability of being left handed if you are a homosexual

What we *want* to know is P(h|l) (probability of being a homosexual if you are left handed). For you Bayes newbies you must resist the temptation to assume that P(h|l) = P(l|h).

By Bayes theorem:

P(h|l) = P(l|h) * P(h) / P(l)

Or

P(h|l) = 6% for dudes and 9% for the ladies.

I'm not sure what use this information is, but you are welcome anyway.