Question

The employees of a firm that manufactures insulation are being tested for indications of asbestos in their lungs. The firm is requested to send three employees who have positive indications of asbestos to a medical center for further testing. If 30% of the employees have positive indications of asbestos in their lungs, find the probability that eleven employees must be tested in order to find three positives. (Round your answer to three decimal places.)

Answer 1

0.070

Explanation:

Y = number on trial

Y has a negative binomial distribution

r = 3

P = 30% = 0.3 probability of positive indication.

P(Y = 11) probability of 11 employees that must be tested to get 3 positives

Y-1Cr-1*p^r*q^(y-r)

Y-1 = 11-1 = 10

r-1 = 3 -1 = 2

10C2 x 0.3³x0.7⁸

45x0.027x0.05764801

= 0.070

This is the probability that 11 employees must be tested to get 3 positives.