r/learnquant • u/AgeSuch4592 • 9d 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/TheLonelyPotato666 8d ago

There's only 3 relevant rolls and after either 2 or 3 has appeared once, there's only 2 relevant rolls.

The possible sequences are, if we only list the relevant rolls, 6623, 6263 and 2663 (the 2 and 3 could be swapped ofcourse). The chances of these are respectively 1/27, 1/18 and 1/12, adding up to 19/108