In a lottery, there are $200$ losing tickets and $10$ winning tickets. We draw with return untill we get our first win. How many times on average do we have to draw to win? Write standart deviation from that value.
Can someone tell me potential reason why I didn't get full points (2 out of 5) for this task with this solution ? I think its correct 100% so I am confused, could please someone verify?
Its obvious geometric distribution so I will use formulas related to them:
$p=\frac{10}{210}=\frac{1}{21}$
$q=\frac{200}{210}=\frac{20}{21}$
$E(X)=\frac{1}{p}=21$
$Var(x)=\frac{q}{p^2}=420$
$\sigma=\sqrt{420}$
We have to draw atleast 21 times to win.