Probability of having six side first I have an exercise as follows: A and B alternately throw a dice (which has six sides numbered from 1 to 6). A starts firstly. What is the probability that A will be the first person who has side 6?
Thanks for any help!

Assuming $A$ throws first:
Prob on 1st throw is $1/6$.  Prob on second throw is $(5/6)^2 1/6$ because both $A$ and $B$ have to fail.  You end up getting a series:
$$\begin{align}\frac{1}{6} + \left(\frac{5}{6}\right)^2 \frac{1}{6} + \left(\frac{5}{6}\right)^4 \frac{1}{6} + \ldots=\frac{1}{6} \frac{1}{1-\left(\frac{5}{6}\right)^2}\end{align}$$
which is $6/11$.
