it long so i put it in the description

Question

An archer has a 25% chance of hitting the bullseye on a target. What is the probability that the archer will hit the bullseye at most three out of five times? Round your percent answer to the nearest hundredth

Answer 1

binomial formula for determining number of successes x in n trials, with probability of success = p:

n!

---- p^x (1-p)^(n-x)

x!(n-x)!

probability of making at most 3 out of 5 bullseyes = 1 - probability of making 4 or 5 bullseyes out of 5.

x = number of bullseyes is a binomial variable, so can use binomial formula to determine the probability x = 4 or 5 in n = 5 shots with p = 0.25 of hitting bullseye:

4 1

5! (0.6) (0.4)

----

4!1!

5 0

5! (0.6) (0.4)

----

5!0!



Add above two computed probabilities then subtract from 1.