Hypergeometric Distribution (Optional): example 4.22

Suppose a shipment of 100 DVD players is known to have 10 defective players. An inspector randomly chooses 12 for inspection. He is interested in determining the probability that, among the 12 players, at most two are defective. The two groups are the 90 non-defective DVD players and the 10 defective DVD players. The group of interest (first group) is the defective group because the probability question asks for the probability of at most two defective DVD players. The size of the sample is 12 DVD players. They may be non-defective or defective. Let X = the number of defective DVD players in the sample of 12. X takes on the values 0, 1, 2, . . . , 10. X may not take on the values 11 or 12. The sample size is 12, but there are only 10 defective DVD players. Write the probability statement mathematically.