1 . Out of 350 applicants for a job, 160 are female and 54 are female and have a graduate degree. If 104 of the applicants have graduate degrees, what is the probability that a randomly chosen applicant is female, given that the applicant has a graduate degree?

2 . Find the probability mass function of a random variableXcorresponding to the absolute value of the difference between the results of two dice.

3 . Suppose 10 fair coins are tossed. Find the probability there will be more heads than tails.

4 . Suppose that a woman is equally likely to have a male or female child. A couple wishes to have exactly three female children in their family. They will have children until this condition is fulfilled.

(a) What is the probability that the family haskmale children?

(b) What is the probability that the family has four children?

(c) What is the probability that the family has at most four children?

5 . Suppose Archana and Katie play a game where they alternate (in this order) in rolling two fair dice until the first person rolls a sum of 8 on a single turn, who wins the game.

(a)Find the probability that each person wins the game.

(b)How much of an advantage does Archana have?

(c)Suppose Archana goes first, then Katie getskturns, and then they alternate. How large mustkbe so that Katie is more likely to win?