Suppose that you purchase randomly select 5 TV sets from a p

Suppose that you purchase (randomly select) 5 TV sets from a production run of 14 TV sets. Of the 14 TV sets, 10 are destined to last at least five years without needing a single repair. What is the probability that 3 of your TV sets will last at least five years without needing a single repair?

Solution

There are 15C4 ways to choose any four TVs.

Meanwhile, there are 11C3 ways to choose three which will last 5 years, and 4 ways to choose a \"defective\" one. Thus, there are (11C3)*(4) ways to do the job.

Thus,

P = [(11C3) * (4)]/[15C4]

= 0.483516484 [ANSWER]