Two presidential candidates, generically labeled D (for Democrat) and R (for Republican), are in a heated election battle. A U. S. presidential election can be broken down into 50 separate subelections, one for each state, and the winner of each subelection is awarded a certain number of points (i. e., electoral votes, the number of which can vary from contest to contest). There are 538 total points available, and so accumulating 270 or more will win the election. Suppose that 43 of the 50 contests have already been more or less decided, and the score is D 244, R 173. Seven contests remain for the nal 121 points. Here is a breakdown which includes how many points each of the remaining contests is worth, along with the probability that each candidate wins that contest

state points P(D wins) P(R wins)
FL 29 0.76 0.24
PA 20 0.82 0.18
OH 18 0.74 0.26
GA 16 0.45 0.55
NC 15 0.66 0.34
VA 13 0.88 0.12
MN 10 0.85 0.15

We will assume2 that the contest in one state is independent of the contests in other states.

Required:
a. There are 2^7 = 128 different win/loss combinations for these last 7 contests. Which ones result in R being elected?
b. What is the probability that R is elected?