```Fall 2007
Math 227
1. Among the eight nominees for two vacancies on a school board are four men and four women.
In how many ways can these vacancies be filled
a. with any two of the eight nominees.
b. with any two of the female nominees.
2. A pizzeria offers 10 toppings for its pizzas. The customer can order any combination of these
toppings, including all of them or none of them. How many different types of pizza are
possible?
3. In how many ways can 10 instructors be assigned to 10 sections of a course in mathematics?
4. In how many different ways can the director of a research laboratory choose two chemists from
among seven applicants and three physicists from among nine applicants?
5. If we roll a pair of dice, what are the probability of getting the sum is
a. an 11.
b. a 5 or a 7.
6. Among 15 applicants for three positions, 10 are college graduates. If the selections are random,
what are the probabilities that the positions will be filled with
a. two applicants with college degrees and one without.
b. three applicants without college degree.
7. What is the probability of getting two aces in a row when two cars are drawn from an ordinary
deck of 52 playing cards, if
a. the first card is replaced before the second card is drawn.
b. the first card is not replaced before the second card is drawn?
8. A civil service examination is prepared so that 80 percent of all persons with a high school
diploma can pass it. Find the probabilities that among 14 persons with a high school diploma
a. at most 10 will pass
b. exactly 12 will pass.
9. If a bank receives on the average of 6 bad checks per day, what is the probability that it will
10. A sample was selected of 506 workers who currently receive two weeks of paid vacation per
year. These workers were asked if they were willing to accept a small pay cut to get an
additional week of paid vacation a year. The following table shows the responses of these
workers.
Yes
No
No Response
Man
77
140
32
Woman
104
119
34
If one person is selected at random from these 506 workers, find the following probabilities.
a. P(Yes | woman)
b. P(no response or man)
11. Assume that women have heights that are normally distributed with a mean of 63.6 inches and
a standard deviation of 2.5 inches. Find the value of the quartile Q3.
12. The diameter of pencils produced by a certain machine are normally distributed with a mean of
0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter
of a randomly selected pencil will be less than 0.258 inches?
13. Assume that the weight loss for the first month of a diet program varies between 6 pounds and
12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform
distribution. Find the probability of that more than 10 pounds were lost.
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