The probability a car salesman sells a car to a customer is 0.05

Question

Assuming the salesmen sees 14 customers in a week, what is the probability he sells less than 3 cars?

Answer 1

n = no sale , s = sale ... less than 3 is 0, 1, or 2

this is binomial ... no sale or sale ... p(n) = .95 ... p(s) = .05

(n + s)^14 = n^14 + 14 n^13 s + 91 n^12 s^2 + ... + 14 n s^13 + s^14

sum the 1st three terms
... .95^14 + (14 * .95^13 * .05) + (91 * .95^12 * .05^2)