There are 90 passengers on a commuter flight from SFO to LAX, of whom 27 are traveling on business. In a random sample of five passengers, use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger.
A).3087
B).1681
C).3602
D).8319

Question

Quizplus · Accepted Answer

The probability of having at least one business passenger in a sample of five can be found by subtracting the probability of having no business passengers from 1. Using the hypergeometric distribution formula, we calculate the probability of having no business passengers and then subtract from 1 for the complement. The calculation is complex and not directly shown, but the correct approach involves using the hypergeometric probability formula or approximating it with a binomial model due to the large population size and relatively small sample size. The correct answer, after performing the calculations, is found to be closest to option D, .8319, indicating a high probability of having at least one business passenger in the sample.

There Are 90 Passengers on a Commuter Flight from SFO