re: Mike and Mike posed an interesting question

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That illustrates my point. If anything, the likelihood of you making it on your 20th attempt is much worse than the likelihood of you making it on your 1st attempt. However, people are acting like they're guaranteed a make if they get enough shots.

It is the same misconception for the people that walk up and drop $500 on black in roulette after 9 straight red numbers. Surely the chances of it being red 10 times in a row are miniscule, ~.1%, but that doesn't mean shite for the 10th spin.

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Although there is surely a dependency (especially because of the increasing pressure and fatigue ), generally speaking, the probability of making the first shot would be close to the probability of making the last shot. So unless you can quantity the dependency and the direction, it would probably be best to treat each as an independent random event with the same probability (e.g., roulette, coin flip, rolling dice). Then as I show above, in this case, you want to find the probability of making at least one shot.