Please help me with

Player A and Player B roll a dice. They roll 5 times each. Who dices "5" first will win the game? If player A plays first, what is prob of Player A winning the game. Is it unfair?

Reply #2 many well be correct. But I cannot read it. That is clearly evidence that serious helpers should know LaTeX.

Let \(\displaystyle X\) be the number of rolls on which the game is over.

Note that \(\displaystyle X=1,2,\cdots,10\).

A wins if \(\displaystyle X=1,3,5,7,9\) and B wins if \(\displaystyle X=2,4,6,8,10\)

So \(\displaystyle \mathcal{P}(X=k)=\left( {\frac{1}{6}} \right)\left( {\frac{5}{6}} \right)^{ k-1} \).