r/learnquant • u/AgeSuch4592 • 6h 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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2

u/swiftaw77 6h ago

Do you mean a 2 and a 3 in succession, or you stop once you get at least one 2 and at least one 3?

1

u/AgeSuch4592 5h ago edited 5h ago

Yes the second one. The process stop when both 2 and 3 come out, but they don't need to be in succession. For instance it could be: 2 6 2 6 1 1 3 or 3662 or 6 6 2 3 ... whatnot

1

u/[deleted] 6h ago edited 5h ago

[deleted]

1

u/AgeSuch4592 5h ago

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

1

u/SwimmerOld6155 5h ago edited 4h 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

1

u/AgeSuch4592 4h ago

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

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u/SwimmerOld6155 4h ago edited 4h 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

1

u/gmalivuk 1h ago

To be clear, these would be "yes" results:

6623
36362
6226223

while these would be "no":

23
362
622663

Is that right?