Lottery variance The chance to win in Lottery game is $0.1$. Michael decided to buy a ticket every week until he will win or until he will buy 5 tickets.
if X is the number of weeks Michael bought a lottery ticket,
what is the variance of $X$?
So I Calculated for X=5, which means LLLLL or LLLLLW. I calculated the probabilities for both, added them up together and then calculated the variance by the formula  $\frac{1-p}{p^2}$. I get $0.798$ which I'm not sure makes sense, am I doing something wrong? Do I need to compute all weeks? Because if so, in the end I get 1. 

Variance in Geometric distribution is $\frac{1-p}{p^2}$. The problem is, it is for infinite number of trials. In your case it is limited by 5, so you need to compute a normalizing constant, so that the probability distribution sums to 1. Once you've done that, you can compute its mean and variance using the formulas you know. 
