Ok so I know most of the reasoning but I just need it explained a bit better because thinking about it is hurtng my brain.
So you have 2 chances of 20% rolls to hit your goal at least once, 2 D5 dice, win condition need one of them to land on 5 would be an example, the chances of either one hitting isn’t 40%, it’s actually more like 36%. I THINK this is because you are hitting 2 out of 2 in some realities so that’s wasted potential, therefore your odds of hitting at least one are lower than 40%… But I really don’t get that last bit at all.
In: Mathematics
With two rolls, you can go through the whole probability tree:
Roll 1 fail & roll 2 fail: 80% * 80% = 64%
Roll 1 success & roll 2 fail: 20% * 80% = 16%
Roll 1 fail & roll 2 success: 80% * 20% = 16%
Roll 1 success & roll 2 success: 20% * 20% = 4%
If you sum up all the cases where you have at least one success, it is 36%.
You can generalize the case when you only want at least once success with the equation 1 – (1-p)^n where p is the chance to succeed and n is the number of rolls. Basically, it rephrases the question to “What are the chances I’ll fail every roll? Then subtract that chance from 100%”
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