A poll taken in Massachusetts in October 2012 showed Obama leading Romney by 60% to 40% in the U. S. presidential race. Let's assume that these numbers represent probabilities. I wished to make a bet with my friend on who would win Massachusetts, and we agreed to base our bet on that poll. I predicted a victory for Obama and would win a profit of $5 if I were right. Assuming we wished this to be a fair game, how much should I have agreed to pay my friend if he was right and Massachusetts went to Romney?

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)