What Keeps Me Up At Night

In the movie Knocked Up, the pregnant woman and her sister try to get into a nightclub and are rejected by the bouncer, who is black. Eventually the bouncer tells them that he's only allowed to let in 5% black people, so for every 25 white people he lets in, he can let in one and a quarter black people. It's actually very funny.

While trying to remember how to fall asleep last night, I noticed that the bouncer's math is wrong. If he lets in 25 whites and 1.25 blacks, then he has let in a total of 26.25 people. But 1.25/26.25 is actually a little under 4.8%. He actually needs to let in 25 × (5% / 95%), or just over 1.3, black people to achieve 5%. Alternatively, if he wants to let in 1.25 blacks (which is 5% of 25), then he needs to let in only 23.75 whites.