Through a purchase card tracking systema local super market

Through a purchase card tracking system,a local super-
market is able to determine who shopped at their store
during any given day.The store is popular,attracting a
steady stream of customers.At the end of each day,store
personnel call 10 customers to find out about their
shopping experience. There are two categories of cus-
tomers:those with no complaints and those with com-
plaints.Any customer who has a complaint,such as not
being able to find a particular product or having to wait
too long in line,is considered a defective for the store.
The store tracks this information and uses it to improve
store operations.While striving for perfection,the store
managers realize that it isn’t possible to make everyone
happy.In the past,the probability of a customer with a
complaint is 0.003.Calculate the probability that on any
evening,two or fewer customers have complaints.

Solution

total customers asked are 10

probability od complaint is 0.003

probability of no complaint is 0.997

probability that 2 or less have complaint = P(0)+P(1)+P(2) = 10C0(0.997)^10(0.003)^0 +10C1(0.003)^1(0.997)^9+10C2(0.003)^2(0.997)^8 = 0.9704