Let's say I have this table of weights:
A: $90\%$
B: $2\%$
C: $3\%$
D: $5\%$
And I have three tries. If one succeeded, it will be taken out of the pool.
How can I calculate the chance that $A$ will occur at least once in $X$ tries?
2026-04-06 05:57:36.1775455056
What is the probability of something having a chance of $90\%$ appear at least once in three tries? Also what is this concept called?
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As far as conceptualizing this, you can think blindly pulling socks from a drawer. 90 are blue, 2 are red, 3 are green, and 5 are black. Imagine you pull a black sock. You would have had a 5/100 chance of doing this, and would remove all black socks after doing so. For your second pull you now have a 2/95 probability of pulling a red sock, 3/95 of a green, and 90/95 of a blue sock.
Consider all of the ways that you could pull three socks out and fail to pull out a blue one.
Black -> Green -> Red
Black -> Red-> Green
etc.
Every other case of pulls has to involve pulling out a blue sock... Hopefully this helps for the early stages of working through this.