An expert shot bits the target 95% of the time. What are the probabilities that he will miss the target: at least one time during fifteen shots

If he hits the target 95% of the time, then you could say that he has a probability of 0.95, or 95% of hitting the target. Let p = the probability of hitting the target or p = 0.95. So you are interested that he misses the target at least once - this could be thought of as not getting a perfect score. So to get a perfect score, it is 0.95 for each target - - 0.95^15 for 15 targets is 0.464. Thus to miss at least one target he needs to NOT have a perfect score - - 1 - 0.464 = 0.536, or 53.6% of happening. Enjoy