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 shots for (i) to be true they will have to miss x times and hit it at the x+1 shot.
So far so good. My problem begins here. They both have a certain chance to hit at but if they don't they have a smaller chance at and so on.
So the final probability is: which is an infinite geometric series. Is that correct?