Probability using the hyper geometric distribution.

The City Transit Authority plans to hire 8 new bus drivers. From the group of 100 qualified applicants, of whom 55 are men and 45 are women, 8 names are to be selected by lot. Suppose that Mary and John Lewis are among the 100 qualified applicants.

(a) i)What is the probability that Mary's name will be selected?

ii) What is the probability that both Mary's and John's names will be selected? (Round your answer to four decimal places)

(b) i) If it is stipulated that an equal number of men and women are to be selected (4 men from the group on 55 men and 4 women from the group of 45 women), what is the probability that Mary's name would be selected? (Round the answer to four decimal places)

ii)What is the probability that Mary's and John's names will be selected? (Round the answer to four decimal places)