Three shoppers from the survey are selected at random, one at a time without replacement. What is the probability that none of the three shoppers purchased office supplies?

Question

An internet research company surveyed 95 online shoppers, each of whom made one purchase today. The company recorded the type of purchase each shopper made. Here is a summary.

Type of purchase Number of Shoppers

Office supplies	18
Electronics	25
Clothing	40
Beauty supplies	12

Three shoppers from the survey are selected at random, one at a time without replacement. What is the probability that none of the three shoppers purchased office supplies?Do not round your intermediate computations. Round your final answer to three decimal places. 

Answer 1

Since the three shoppers from the survey that are being selected at random are being drawn one at a time without replacement, the probability of selecting a shopper from the survey that did not purchase office supplies will be different for each of these three shoppers. By the Multiplication Rule for Probabilities and the fact that 95 - 18 = 77 of the shoppers from the survey did not purchase office supplies, we have that

P(none of the the three shoppers purchased office supplies) = (77/95)*(76/94)*(75/93)

= 438900/830490

= 0.528