Mike Vanderjagt is the most accurate kicker in the history of professional football. He makes 91.2% of his field goal attempts. What is the probability that he will miss at most 1 out of the next 4?

Answer 1

prob(miss none) = C(4,0)(.088)^0 (.912)^4 = ...
prob(miss one) = C(4,1)(.088)(.912)^3 = ..
add them up

Answer 2

p success = .91
p fail = .09
chances of missing zero + chances of missing one
4C0 = 1
so
1 * .09^4 * .91^0 = .09^4 = 6.56*10^-5

4C1 = 4!/[3!] = 4
so
4*.09^3*.91 = .00265

.00265 +.0000656 = .00272