In blasting soft rock such as limestone, the holes bored to hold the explosives are drilled with a Kelly bar. This drill is designed so that the explosives can be packed into the hole before the drill is removed. This is necessary since in soft rock the hole often collapses asthe drill is removed. The bits for these drills must be changed fairly often. Let X denote the number of holes that can be drilled per bit. The density for X is given by the table: x 1 2 3 4 5 6 7 8
f(x) .02 .03 .05 .2 .4 .2 .07 (?)

a. Find f(8).
b. Find the table for F.
c. Use F to find the probability that a randomly selected bit can be used to drill between three and five holes inclusive.
d. Find P[X < 4] and P[X < 4]. Are these probabilities the same?
e. Find F(-3) and F(10).

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.)