probability

Question

A sample of

50 homeowners who recently hired a landscaping service yielded the following information about their landscaper.


Number of Homeowners
Would you Recommend Your Landscaper to a Friend
30
Yes
12
No
8
Not sure
Three homeowners who provided information for the table were selected at random. Determine the probability that they would all recommend their landscaper.

Answer 1

The probability will be provided by an extended hypergeometric distribution, sometimes call multinomial...except that you only need one set of choices:

 

₃₀C₃/₅₀C_{3 = 30*29*28/(50*49*48)}

_{This assumes that the sample was done without replacement!}