Name:
Student #:
Quiz 2
Duration: 50 min
Total: 10 Marks
1. (1 Mark) A survey of an insurance company’s medical policyholders in the last three years
revealed the following information:
• 31% made claims for dental care
• 27% made claims for optical care
• 21% made claims for other medical care
• 15% made claims for dental and optical care
• 13% made claims for optical and other medical care
• 11% made claims for dental and other medical care
• 7% made claims for all three sorts of care
Calculate the percentage of the medical policyholders that made none of the three types of
claims during the last year.
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2. Calculate the number of possible distinct arrangements of the letters in the following words:
(a) (1 Mark) MASSACHUSETTS
(b) (1 Mark) SASKATCHEWAN
3. Let A = {2, 3, 5, 7}, let B = {1, 3, 5, 7, 9}, and let the universal set S = {1, 2, , . . . , 10}.
Determine:
(a) (0.5 Mark) A ∩ B
(b) (0.5 Mark) A ∪ B c
(c) (0.5 Mark) (A ∪ B)c
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4. (1.5 Marks) A sport team are known to be a weak road–trip team. They win just 35%
of the games that they play as the road team. Just before a seven–game road trip, team
management informs the coach that unless the team wins at least three of these seven games,
he will be fired at the conclusion of the road trip. Assuming that the outcomes of different
games are independent, calculate the probability that the coach is fired at the end of this
trip.
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5. (1.5 Marks) An urn contains four balls numbered 1–4. The ball are randomly drawn one–
by–one without replacement. Calculate the probability that ball 2 is drawn before balls 3
and 4.
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6. (1.5 Marks) George is taking a sociology class that has 24 students, including himself. For a
group project the class will be randomly divided into 8 equal size groups of 3. What is the
least number of friends he must have in the class so that there is at least a 50% chance of
having at least one of his friends is in his group?
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7. (1 Mark) Members of a pension plan are required to select 3 equity funds and 2 bond funds
in which to invest their retirement savings. If there are 10 equity funds and 6 bond funds
available, how many choices are possible?
Hint: They cannot double–pick the same fund.
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