Hypergeometric Distribution · Example 2

Suppose a shipment of 100 laptops is known to have ten defective laptops. An inspector randomly chooses 12 for inspection. He is interested in determining the probability that, among the 12 laptops, at most two are defective. The two groups are the 90 non-defective laptops and the 10 defective laptops. The group of interest (first group) is the defective group because the probability question asks for the probability of at most two defective laptops. The size of the sample is 12 laptops. (They may be non-defective or defective.) Let X = the number of defective laptops 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 laptops. Write the probability statement mathematically.

OpenStax, Introductory Statistics 2e · §4.5 Hypergeometric Distribution · Example 2