At most probability question:

Question

In the Olympic sport of biathlon, athletes must cross country ski and then shoot a rifle at a small circular target. Two athletes shoot one shot each at the target independently. The probability of each player hitting the centre target is 0.55 and 0.65 respectively. What is the probability that at most one of them will hit the centre. Show all work.

Answer 1

We are told we have independence here. If A and B are independent events, then P(A and B) = P(A)*P(B).

Note that "at most one" means "less than or equal to one", so you want the probability of the following events:

(a) player A misses AND player B misses.

(b) player A hits the center AND player B misses.

(c) player A misses AND player B hits the center.

(I was very suggestive with the use of "and").

These situations do not overlap, so the probability of (a) or (b) or (c) happening is just the sum of the individual probabilities. Figure those out, add them and you're done.

Can you continue?