Probability of Condom Failure

As per CDC, male condoms as a contraceptive has a failure rate of 13% for typical use and 3% for perfect use. The question is: what does it mean? The website doesn’t clarify further.

Possibility 1: a woman will get 13% of the times she has sex using a condom.

If that is true, using the protection once a month (during fertile days), a binomial equation tells you there is an 81% chance of getting pregnant in a year; (1 – (1-0.13)12)*100 = 81. It is no different from the approximate chances of conception for a woman without fertility issues.

The correct interpretation of the statistic is that it’s the number of pregnancies when 100 women use that birth control method for one year. Putting the number 0.13 back in the binomial equation, one can get the condom failure probability of about a per cent. That is pretty impressive.

1 – (0.988)12 = 0.13

References

Contraception: CDC
Statistically safe sex: Math Careers
Interpreting Birth Control Failure Rates: Very well health
Chances of getting pregnant: Medical news today
Risk Savvy: Gerd Gigerenzer