A shipment of 50 mechanical devices consists of 42 good ones

A shipment of 50 mechanical devices consists of 42 good ones and eight defective. An inspector selects five devices at random without replacement. What is the probability that at most four are good? Hint: Use the compliment rule when solving this problem to make it a lot easier.

Solution

There are 50C5 ways to choose any 5 units.

Note that

P(at most 4 are good) = P(at least 1 defective) = 1 - P(no defective)

Thus, there are 42C5 ways to choose nondefective units.

Thus,

P(at most 4 good) = 1 - P(no defective) = 1 - 42C5 / 50C5

P(at most 4 good) = 0.598506674 [ANSWER]