The City Transit Authority plans to hire 14 new bus drivers. From a group of 100
ID: 2922090 • Letter: T
Question
The City Transit Authority plans to hire 14 new bus drivers. From a group of 100 qualified applicants, of whom 65 are men and 35 are women, 14 names are to be selected by lot. Suppose that Mary and John Lewis are among the 100 qualified applicants.
(a) What is the probability that Mary's name will be selected?
(b)What is the probability that both Mary's and John's names will be selected? (Round your answer to four decimal places.)
(c)(b) If it is stipulated that an equal number of men and women are to be selected (7 men from the group of 65 men and 7 women from the group of 35 women), what is the probability that Mary's name will be selected? (Round your answer to four decimal places.)
(d)What is the probability that Mary's and John's names will be selected? (Round your answer to four decimal places.)
Explanation / Answer
a. There are 100 applicants, and 14 drivers has to be selected. Thus, the probability that Mary's name is selected is 14/100=0.14.
b. Out of 100 applicants, if 14 drivers are selected, the probability that John is one of the 14 drivers is 0.14. Therefore, probability that both Mary and John are selected are 0.14*0.14=0.0196
c. If 7 women are to be selected from 35 women, then probabilty that Mary's name is included is 7/35=0.2.
d. Equivalently, out of 65 men, if 7 are to be selected, probability that John's name is included is 7/65. Thus, probability that both Mary's and John's names will be selected is 7/65*7/35=0.0215