   SEARCH HOME Math Central Quandaries & Queries  Question from Jessica, a student: Hi, ive tried this question and just wanted to check with you if my method is correct or not. Question: A small mobile phone retailer has found that one of their phones has a 12% probability of being faulty and a replacement having to be provided for the customer. They have just received a trial order for 10 phones from their biggest customer who will take their business elsewhere if 20% or more items are faulty. i) what is the probability that they will lose their biggest customer? I used the binomial distribution formula using n=10, x=2, and p=0.12. i got the answer 0.233043 (23.3%). is this correct? Thanks Jessica Jessica,

You found the probability that exactly 2 are defective. They will lose the customer if the number defective is 2 or 3 or 4 or ... or 10. It's easier to calculate the probability that they won't lose the customer.

Suppose P(X) is the probability that exactly X of the phones are defective. The probability that they will not lose the customer is then

P(0) + P(1).

The probability they will lose the customer is then

1 - [P(0) + P(1)].

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.