I've run into a more difficult problem that I'll simplify in this example:
Let's say we give 100 participants 3 attempts to make a hoop from the 3 point line on a basketball court. The participants are categorized by their first successful shot. The results are:
- 50 make it on the 1st shot
- 30 make it on the 2nd shot
- 10 make it on the 3rd shot
- 10 never make the shot (after 3 attempts)
It's easy to calculate, of those who make the shot, on average, it takes 1.55 shots to make a successful shot from the 3 point line. My question is: How do I factor in the participants that never make the shot?
Disclaimer: This is my first post in this stack exchange, sorry if I broke the rules.
Another approach is to use the available data to find success probability $p$ for a geometric distribution. For example, if $p=.5,$ then your four counts might be about $50, 25, 13, 12,$ instead of $50, 30, 10, 10,$ respectively. Then the average number of tries until success would be 2.
Maybe you can get a better estimate for $p$ than my rough guess that $p = 0.5.$