Question

a company knows that 11% of it customers are retirees. find the probability that if 6 of this companys customers are randomly selected, at least one of them is a retiree.

1.771561e - 6
5.34
0.496981290961
0.89
0.999998228439
0.503018709039

Explanation:

Step1: Find probability of non - retiree

The probability that a customer is not a retiree is $1 - 0.11=0.89$.

Step2: Find probability that none of 6 is a retiree

Since the selections are independent, the probability that none of the 6 randomly selected customers is a retiree is $(0.89)^6$.
$(0.89)^6=0.503018709039$.

Step3: Find probability that at least one is a retiree

The probability that at least one of the 6 customers is a retiree is $1 - P(\text{none is a retiree})$.
$1-(0.89)^6 = 1 - 0.503018709039=0.496981290961$.

Answer:

0.496981290961