Finite Help!!!!!!!

Question

Rework problem 23 from section 4.1 of your text involving a basketball player's three point shooting. Assume that his shots are Bernoulli trials, and that he makes 1 in 4 of his shots.

How many three point shots must the player attempt so that the probability of his hitting at least one of them is at least 0.99? 

Answer 1

Look at it from the opposite direction: how many shots must he take that his chance of having not made any of them drops to 0.01? Since these are considered Bernoulli trials, each shot either succeeds or fails and the probability of failure is 0.75. So, it would take x shots to drop the probability of missing all of them to 0.01 or

0.01 = 0.75^x

You can then solve for x, which will also be the number of shots needed to have a 0.99 probability of succeeding at least once (since the probability of missing all x shots + probability of succeeding at least once after x shots = 1)