September 21, 2012
1. Suppose a pair of fair dice is rolled 20 times as part of a game of Monopoly,
and each time the pair is rolled, their sum is observed.
(a) What is the chance that a seven was observed on exactly 4 rolls among the 20?
(b) What is the chance of observing less than 4 sevens?
(c) What is the chance of between 1 and 5 sevens, inclusive?
2. The rock radio station WBIN has about 2500 CD's in its library, with 65% of the CD's being
classified as Classic Rock and 35% classified as Alternative. A DJ on the all-night shift, wanting
a good mix of classic and alternative, chooses 10 CD's at random from the library.
(a) What is the probability that exactly 5 CD's are classic rock, and 5 CD's are alternative?
(b) What is the probability that all 10 CD's are of the same genre (i.e. either all classic or all alternative)?
(c) What is the probability that at least one CD is alternative?
(d) What is the probability that less than 3 CD's are alternative?
(e) What is the probability that the number of classic rock CD's chosen is between 5 and 7, inclusive?