Simulation for Probability of Success

Imagine that you try to do something and there’s a 20% chance of success. If you try to do the thing six times, what is the probability that you succeed at least once?

Andrew Huberman made the mistake of doing math on the fly, and said the chances summed to 100%, which is absolutely certain, after five tries. It was in the context of trying to get pregnant. Huberman said that if there’s a 20% chance of getting pregnant, then there must be something wrong if you don’t get pregnant after five or six tries.

Probability doesn’t work like that. Otherwise, casinos would not exist.

Here is a ten-by-ten grid of 100 squares:

Pick a square at random, and there’s a 20% chance that you select a black square. There is an 80% chance that you select a gray square.

In the interactive chart below, make the random picks to see where the final probability converges to.

Simulating Your Chances of Success

If there’s a chance, with enough tries, you approach near certainty.

For six attempts at a 20% success rate, 74% succeed at least once. So it’s not quite certain, but if you increase the number of attempts, you can get pretty close. Even with lower a success rate, the chance of succeeding at least is still high with enough attempts.

Of course, this is all I can think about now:

If you want to get into the details of the example, read about binomial distributions.