Final answer:
The probability that no employee in the sample work at the plant in Hawaii is 0.0279, the probability that one of the employees in the sample works at the plant in Hawaii is 0.2656, the probability that two or more of the employees in the sample work at the plant in Hawaii is 0.7065, and probability that nine of the employees in the sample work at the plant in Texas is 0.06.
Step-by-step explanation:
To find the probability that none of the employees in the sample work at the plant in Hawaii, we need to find the probability of selecting 0 employees from the Hawaii plant out of a total sample size of 10 employees. Since there are 20 employees at the Hawaii plant and 60 employees in total, the probability is:
P(selecting 0 employees from Hawaii) = (20C0 * 40C10) / (60C10) = 0.0279
To find the probability that one of the employees in the sample works at the plant in Hawaii, we need to find the probability of selecting 1 employee from the Hawaii plant out of a total sample size of 10 employees. The probability is:
P(selecting 1 employee from Hawaii) = (20C1 * 40C9) / (60C10) = 0.2656
To find the probability that two or more of the employees in the sample work at the plant in Hawaii, we need to find the probability of selecting 2 or more employees from the Hawaii plant out of a total sample size of 10 employees. The probability is:
P(selecting 2 or more employees from Hawaii) = 1 - P(selecting 0 employees from Hawaii) - P(selecting 1 employee from Hawaii) = 1 - 0.0279 - 0.2656 = 0.7065
To find the probability that nine of the employees in the sample work at the plant in Texas, we need to find the probability of selecting 9 employees from the Texas plant out of a total sample size of 10 employees. The probability is:
P(selecting 9 employees from Texas) = (40C9 * 20C1) / (60C10) = 0.06