Birth Control Statistics in GNU Octave

Hello!  A fun thought occurred to me while looking over an old statistics textbook -- how effective is our birth control?

For the sake of argument, lets say that condoms, used properly, have a 97% effective rate.  A birth control pill, properly used, have a 99% effective rate.  Those may sound high, but they aren't really.  Lets take a look and assume you are having sex once a week for two years. What is the likelihood that you will have at least one condom break, the pill be ineffective, or both failing simultaneously? Rut Roe!

Since each condom use can be considered an independent test, the probability of failure is 1 - 0.97, or 3% chance of failure.  Similarly, the pill would have a 1% chance of failure.  The data is as follows:

Probability of faulty birth control method over time

What does this graph tell us?  It is 1- (the chance of getting X amount of condoms in a row that are successful), or  the ever increasing chance that your next condom / birth control pill, combination will be faulty.  As the blue line shows, over two years, or 104 condom uses, you have a ~95% chance of one of those condoms being defective and failing.  With straight birth control and 104 tests, you have a 63% chance that at least one time it did not work.   The best though, is the redundant method: The chance that during a two year period that both the condom and the birth control would fail at exactly the same time.  This would be the same as modeled as a system in parallel:
 (1 - 0.03*0.01) = 99.7% individual chance of success with some kind of protection in parallel system per sexy times.  Hooray.  The green line shows that over 104 weeks,  the chance of double failure is nearly negligible.  This is the way to be!

So wait wait wait, a failed condom or birth control pill does not necessarily mean pregnancy occurs.  Every menstrual cycle, there are about ~5 days of which sperm in the system could meet an egg.  5 days out of every 28, or ~18% of all days in a year.  This reduces the 1 / week for 104 week chance of issue significantly, as the following graph shows:

This graph basically states that, having random sex once / week, over two years, presents a 17% chance of a condom breaking while in ovulation, a 11% chance of the pill not working during ovulation, and basically a 0% chance of the pill and the condom breaking at exactly the same time.

Lesson in all of this?  Redundancy in parallel systems is the way to go.