A box contains 3 red marbles and 3 yellow marbles. Consider the two–stage experiment of randomly selecting a marble from a box, replacing it, and then selecting a second marble. Determine the probabilities of the following events: a. Selecting 2 red marbles.

P (red) =

b. Selecting a red marble on the first draw and a yellow marble on the second.

P (red then yellow) =

c. Selecting at least 1 yellow marble.

P (at least 1 yellow) =

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.)