# A and B roll a dice taking turns with A starting this process. Whichever one rolls the first 6, wins. Find the probability of A winning.

Stephany Wilkins 2022-10-23 Answered
ALternate solution to a probability problem
A and B roll a dice taking turns with A starting this process. Whichever one rolls the first 6, wins. Find the probability of A winning.
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Step 1
Let p be the probability of A winning. If A doesn't win with the first move, it is as if A and B had swapped their roles.
Step 2
Thus, $p=\frac{1}{6}+\frac{5}{6}\left(1-p\right)$