Question

Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 45 employees; the Hawaii plant has 15. A random sample of 10 employees is to be asked to fill out a benefits questionnaire. 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

Answer:

a) The probability that none of the workers of the sample work in Hawaii is 0.04231

b) The probability that 1 worker of the sample works at the plant in Hawaii is 0.1763

c) The probability that 2 or more employees in the sample work in Hawaii is 0.7814

d) THe probability that 9 of the employees in the sample work at the plant in Texas is 0.1763

Step-by-step explanation:

a) The probability that none of the employeees in the sample work in Hawaii can be computed as follows: First, we have 15 employees in Hawaii from 60 total, so the probability that the employee doesnt work in Hawaii is 45/60. For the second one is 44/59, because we have 1 less case and that is someone in texas. For the third one is 43/58 and so on. Thus, the probability that all 10 workers are not from Hawaii is

45/60*44/59*43/59*42/57*41/56*40/55*39/54*38/53*37/52*36/51 = 0.04231

b) Lets start by computing the probability that the first employee is from Hawaii and the rest now. We have 60 workers, 15 from hawaii, thus, the porbability that the first one is from Hawaii is 15/60 = 1/4. From the remaining 59 workers, 45 are not from Hawaii, therefore, the probability that the second worker is not from Hawaii is 45/59. For the third one the probability is 44/58 and so on, therefore, this probability is

1/4*45/59*44/58*43/57*42/56*41/55*40/54*39/53*38/52*37/51= 0.01763

Since the worker in Hawaii can be any of the 10 in the sample, we should multiply this result for 10 to obtain the probability that exactly 1 worker in the sample works in Hawaii. As a result, the probability that 1 worker of the sample works in Hawaii is 0.01763*10 = 0.1763.

c) The probability that at 0 or 1 workers are from Hawaii is the complementary event of the probability that 2 or more workers in the sample work in Hawaii. Thus, we can obtain this probability by summing the probability that 0 workers are from Hawaii with the probability that 1 workers is from Hawaii and substract that result from 1. Thus, the probability that 2 or more workers work in the plant of Hawaii is 1-(0.1763+0.04231) = 0.7814

d) The event '9 of the employess work at texas' is the exact same event that '1 worker is from Hawaii', therefore the probability of this event is exactly the same than the porbability computed in b), in other words, it is 0.1763