Question

Video Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 50 employees; the Hawaii plant has 20. A random sample of 10 employees is to be asked to fill out a benefits questionnaire. Round your answers to four decimal places. a. What is the probability that none of the employees in the sample work at the plant in Hawaii? b. What is the probability that 1 of the employees in the sample works at the plant in Hawaii? c. What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii? d. What is the probability that 9 of the employees in the sample work at the plant in Texas?

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Number of employees in Texas plant = 50

Number of employees in Hawaii plant = 20

Total number of employees = 50 + 20 = 70

a. P(none of the employees work in Hawaii plant) = P(all employees are from Texas plant)

= 50C10/70C10

= 0.0259

b. P(1 employee in Hawaii) = P(9 employees from Texas and 1 from Hawaii)

= 50C9 x 20C1 / 70C10

= 0.1263

c. P(2 or more employees from Hawaii) = 1 - [P(none of the employees work in Hawaii plant) + P(1 employee in Hawaii)]

= 1 - (0.0259 + 0.1263)

= 0.8478

d. P(9 employees from Texas) = P(1 employee in Hawaii)

= 0.1263