[SOLVED] Probability problem check please

Two people are shooting at a target. They both have a chance of 0.2 to hit the target. Find:

(i) What is the probability that they will hit the target at the same time.

(ii) What is the probability that they will hit the target at different times.

I have tried to solve only (i) so far but I suppose the algorithm is the same for (ii). Here is what I have:

After $\displaystyle x+1$ shots for (i) to be true they will have to miss x times and hit it at the x+1 shot.

$\displaystyle {(0.8^x \space \times 0.2)}^2 \; x \in [0,\infty]$

So far so good. My problem begins here. They both have a certain chance to hit at $\displaystyle x=n$ but if they don't they have a smaller chance at $\displaystyle x=n+1$ and so on.

So the final probability is:$\displaystyle \sum_{i=0}^{\infty} {(0.8^i \space \times 0.2)}^2$ which is an infinite geometric series. Is that correct?