Tutorial 4
Feb 21-24
1. A person is dealt 5 cards from a deck of 52 cards. What is the probability they are all clubs?
2. A pair of dice is thrown. What is the probability that one of the faces is a 3, given that the sum of the
two faces is 9?
3. Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer.
25 percent who buy beer buy cigars. Determine the probability that a customer buys beer.
4. If a product is made using five individual components, and P(product meets specifications) = P(E)
= .98, what is the probability of an individual component meeting specifications, assuming that this
probability is the same for all five components?
5. If P(A|B) = .2 and P(B) = .8, determine the intersection of events A and B.
6. Chauncey Billups, a current shooting guard for the Los Angeles Clippers, has a career free-throw
percentage of 89.4%. Suppose he shoots six free throws in tonight’s game. What is the probability
that Billups makes five or more of his free throws?
1
7. There are currently 18 pit bulls at the pound. Of the 18 pit bulls, four have attacked another dog in
the last year. Joe, a member of the staff, randomly selects six of the pit bulls for his group. What is
the probability that exactly one of the pit bulls in Joe’s group attacked another dog last year?
8. Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA
candidates is selected. What is the probability that at least one of them has a degree in economics?
9. Suppose a baseball team has 14 players on the roster who are not members of the pitching staff. Of
those 14 players, assume that three have recently taken a performance-enhancing drug. Suppose the
league decides to randomly test five members of the team. What is the probability that at least one of
the tested players is found to have taken a performance-enhancing drug?
10. Suppose your firm is buying five new computers. The manufacturer offers a warranty to replace any
computer that breaks down within five years. Suppose there is a 25% chance that any given computer
breaks down within five years. Suppose the warranty for five computers costs $700, while a new
computer costs $600. Is the warranty less expensive than the expected cost of replacing the broken
computers?
11. A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot
segment of this roll is two. What is the probability of no defects in 10 feet of steel?
12. According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude
of 6.5 or greater every 100 years. What is the probability that no earthquakes with a magnitude of 6.5
or greater will strike the San Francisco Bay Area in the next 40 years?
2