From a group of 100 qualified applicants, of whom 65 are men and 35 are women, 12 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 both Mary's and John's names will be selected? (Round your answer to four decimal places.)
b)If it is stipulated that an equal number of men and women are to be selected (6 men from the group of 65 men and 6 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.)
What is the probability that Mary's and John's names will be selected? (Round your answer to four decimal places.)

Question

From a group of 100 qualified applicants, of whom 65 are men and 35 are women, 12 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 both Mary's and John's names will be selected? (Round your answer to four decimal places.)
b)If it is stipulated that an equal number of men and women are to be selected (6 men from the group of 65 men and 6 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.)
What is the probability that Mary's and John's names will be selected? (Round your answer to four decimal places.)