# Bad Math about Infertility in the WSJ

From the *Wall Street Journal*:

Infertility, defined as the inability to conceive after one year of unprotected sex, affects one in six couples of childbearing age in the U.S. In 40% of cases, the problem is with the man; in 40% it’s with the woman, and in 20%, something is amiss with both, say Zev Rosenwaks and Marc Goldstein, fertility experts at New York Presbyterian/Weill Cornell Medical College and co-authors of the 2010 book, “A Baby at Last!”

Probability is often confusing, but after running the numbers, I’m fairly certain this math is wrong. If we assume that infertility affects one in six couples, then 5/6 pairings are fertile. Assuming that people choose who they try to have children with independent of fertility, at least initially, and assuming the infertility can be equally due to either the man or the woman, the results follow quite clearly: only about 5% of cases of infertility are due to both members of the couple being infertile, while the other 95% of the time it’s either due to the man or woman only.

Anyone know how the WSJ numbers were calculated?

*How my calculations were done: if 5/6 pairings are fertile, this means that the square root of 5/6, or about 91%, of the population is fertile. Of those pairings then that result in infertility (that remaining 1/6), the ones that are due to both the man and woman being infertile are only (1-0.91)^2/(1/6), or about 5%.*