Probability

Question

A company guarantees customer satisfaction or the company will refund the purchase price of the product. Previous experience has shown that 9% of the purchases are returned. What is the probability that no more than 1 of the next 6 purchases will be returned?

Answer 1

This is a binomial probability problem. Assuming 6 trials (each purchase is a trial), the probability of a success ( a return) is 9% or 0.09. The probability of "no more than one" return is the probability of exactly zero returns plus the probability of exactly one return.

P(0) = 6C0 * (0.09)^0 * (0.91)^6 = 6!/(6-0)! * 1 * (0.91)^6 = (0.91)^6 = 0.567869252

P(1) = 6C1 * (0.09)^1 * (0.91)^5 = 6!/(6-1)! * 0.09 * (0.91)^5 = 0.3369773584

" the probability that no more than 1 of the next 6 purchases will be returned"

P(x<=1) = P(0) + P(1) = 0.567869252 + 0.3369773584 = 0.9048466104

Or, using a TI-84:

binomcdf(6,0.09,1) = 0.9048466104