Winter 2010 Final Exam 201-301RE
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1. A political scientist asked a group of people how they felt about two political policy statements. Each
person was to respond A (agree), N (neutral), or D (disagree) to each policy statement. [4]
a. Describe the sample space; that is, list all possible response combinations to the two statements.
b. Assuming each response combination in the sample space is equally likely, what is the probability
the person being interviewed agrees with at least one of the two policy statements?
c. Assuming each response combination in the sample space is equally likely, what is the probability
the person being interviewed agrees with exactly one of the two political policy statements?
d. Assuming each response combination in the sample space is equally likely, what is the probability
the person being interviewed agrees with the two political policy statements?
2. An interior decorator must furnish two offices. Each office must have a desk, a chair, and a file cabinet . At
a local office furniture store there are 6 models of desks, 8 models of chairs, and 4 models of file cabinet ,
all of which are compatible. (Any desk can be matched with any chair, etc.) [4]
a. How many choices does the decorator have if he wants to select two desks, two chairs, and two file
cabinets if he doesn’t want to select more than one of any model?
b. How many ways can he hire two technicians with different salaries from a group of 20 all equally
qualified ?
3. Ryan prepares for an exam by studying a list of 20 problems. He can solve 12 of them. For the exam, the
instructor selects ten questions at random from the list of twenty. [6]
a. In how many ways can 10 problems be chosen from the 12 that Ryan can solve?
b. In how many ways can the 10 problems be chosen from all the 20 problems on the list?
c. What is the probability that Ryan can solve all ten problems on the exam?
4. We must form a four-digit number using the digits 1, 2,3,4,5 without repetitions. How many numbers can
be created? [2]
5. A group of forty people at a health club were classified according to their gender and smoking habits, as
shown in the table below. One person is selected at random from that group of forty people. [7]
Smoking Habits
Gender
Smoker (S)
Nonsmoker (N)
Total
Male (M)
2
24
26
Female (F)
6
8
14
Total
8
32
40
a. What is the probability the person does not smoke?
b. What is the probability the person is female?
