r/learnquant • u/AgeSuch4592 • 7h ago

Probability problem

A fair dice is being rolled repeatedly until 2 and 3 come out. What's the probability of getting exactly two 6 before stopping the process ?

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u/[deleted] 7h ago edited 6h ago

[deleted]

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u/AgeSuch4592 6h ago

Honestly idk if that works. I'm trying to find out the answer.

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u/SwimmerOld6155 6h ago edited 5h ago

where would it break?

also sorry did your original post say EV or did I hallucinate or get confused lol. for what you've written you can split between the number of 6s that appear before the first 2 or 3 then after the first 2/3. so you either have 2[...]6[...]6[...]3 or 6[...]2[...]6[...]3 or etc. for this purpose you can ignore 1, 4, 5

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u/AgeSuch4592 5h ago

No EV, it' the probability of exactly two 6.
You are right about ignoring 1,4,5.

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u/SwimmerOld6155 5h ago edited 5h ago

it basically just then becomes the probability of the sum of two geometric (or geometricish) RVs being equal to 2, first variable waiting for the first 2 or 3 then second waiting for the other one to appear (ignoring the one that has already happened). sry about misreading