O’Brien Sp10
FM EC Problems
Finite Mathematics Extra Credit Problems
Each problem, correctly worked out, with appropriate support work shown, is worth one point.
The maximum number of extra credit points you can earn for the semester is 10.
1.
Boats In The Sun manufactures two kinds of inflatable boats, two-person boats and four-person boats.
Each two-person boat requires 0.9 labor-hours in the cutting department and 0.8 labor-hours in the
assembly department. Each four-person boat requires 1.8 labor-hours in the cutting department and
1.2 labor-hours in the assembly department. The maximum labor-hours available each month in the cutting
and assembly departments are 864 and 672, respectively. In addition the distributor will not take more than
750 two-person boats each month. The company wants to determine a production schedule that will
maximize the monthly profit. If the company anticipates making a profit of $30 on each two-person boat and
$50 on each four-person boat, how many boats of each kind should be manufactured each month to
maximize the profit?
2.
An appliance store sells two brands of televisions. Each Daybrite set sells for $425, and each Noglare set
sells for $700. The store’s warehouse capacity for television sets is 350, and new sets are delivered only
one each month. Records show that customers will buy at least 70 Daybrite sets and at least 180 Noglare
sets each month. How many of each brand should the store stock and sell each month to maximize
revenue?
3.
Peggy made a down payment of $500 toward the purchase of new furniture. To pay the balance of the
purchase price, she has secured a loan from her bank at 7.89% per year compounded monthly. Under the
terms of her finance agreement, she is required to make payments of $75.67 at the end of each month for
24 months. What was the purchase price of the furniture?
4.
A company has an immediate need for a loan. In an agreement worked out with its banker, the company
assigns its royalty income of $4800 per month for the next 3 years from certain oil properties to the bank,
with the first payment due at the end of the first month. If the bank charges interest at the rate of 9% per
year compounded monthly, what is the amount of the loan negotiated between the parties?
5.
The Meek brothers are planning a trip around the world. They hope to work some as they go, but believe
that they should have accessible $800 per month so they can live in relative comfort for the year they plan
to be gone. How much should they have in an account earning 6% compounded monthly when they
leave so that they can withdraw the desired $800 each month for twelve months?
6.
A group of people were surveyed about what media source they use to get news about their community.
It was found that 134 read only the paper, 231 watch only TV, 39 listen to the radio and watch TV, and
4 read the paper, watch TV and listen to the radio. It was also found that 371 watch TV, 279 read the paper,
96 listen to the radio, and 5 do not use any of the three media sources mentioned here to get news about
their community. How many people surveyed:
a.
read the paper and watch TV?
b.
read the paper and listen to the radio only?
c.
watch TV or listen to the radio?
d.
use exactly two of the three media sources to get news about their community?
e.
listen to the radio or watch TV, but don’t read the paper?
f.
use exactly two of the three media sources mentioned here?
g.
use at least two of the three media sources mentioned here?
h.
use at most 1 of the three media sources mentioned here?
7.
Let A = {Joe, Bill, Sarah, Kathy, Michael, Gary, Amanda, Grant, Nicole, Connie},
B = {Michael, Jim, Ethel, Connie, Randy}, and
C = {Frank, Randy, Millie, Joe, Jim, Grant}
a.
Find n( C  A  B ).
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FM EC Problems
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b.
In how many ways can a 6 person sample be selected from set A?
c.
In how many ways can set B select a four person team consisting of a president, vice-president,
secretary and historian?
8.
Morse code uses a sequence of dots and dashes to represent letters and words. How many sequences are
possible with at most 3 symbols?
9.
In how many ways can a full house of aces and eights (3 aces and 2 eights) occur in 5-card poker?
10.
A code consists of 4 digits followed by 4 letters.
a.
How many codes are possible? Repetition is allowed.
b.
How many codes are possible if digits cannot repeat?
c.
How many codes are possible if the first digit can’t be 0, the first letter can’t be O or I and neither digits nor
letters can repeat?
11.
A little league baseball coach always has the pitcher bat last and the homerun hitter is always fourth, then
how many batting orders are possible from nine given players?
12.
An electronics store receives a shipment of 30 graphing calculators, including 3 that are defective. Five of
these calculators are chosen at random to be sent to a local high school. How many selections contain:
a.
3 defective?
b.
1 defective?
c.
at least 1 defective?
d.
at most 3 defective?
13.
A committee of 8 members is to be made from a club that is made up of 21 members, 11 women and
10 men. What at the odds that at least 6 men will be chosen to be on the committee?
14.
In how many ways can five boys and three girls be seated in a row if
a.
Boys and girls are seated alternately?
b.
Boys sit together and girls sit together?
c.
One of the girls, Sue, must be seated on the left end?
15.
Twenty-six cards, each containing exactly one letter of the English alphabet, are well-shuffled and put in a
box. One card is pulled out, its letter recorded (in the order in which the card was drawn), and the slip is
replaced. This is done 5 times, Find the probability that LORIE is formed.
16.
In a survey of 1000 eligible voters selected at random, it was found that 62% had a college degree.
Additionally, the survey results showed that of the eligible voters who had a college degree, 85% voted in
the most recent senatorial election. Furthermore, only 42% of the eligible voters without a college degree
voted in the same election. Based on this information and assuming it is representative of the general
voting population, find the probability that a randomly selected eligible voter:
a.
has a college degree and did not vote in the last senatorial election.
b.
does not have a college degree if it is known that s/he did not vote in the last senatorial election.
17.
According to readings in business publications, there is a 50% chance of a booming economy (B) next
summer, a 20% chance of a mediocre economy (M), and a 30% chance of a recession (R). The probability
that a particular type of investment will produce a huge profit (H) in a booming economy is .1, .6 in a
mediocre economy, and .3 in a recession. If the investment does produce a huge profit, what is the
probability that the economy is mediocre?
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FM EC Problems
18.
A shipment of computer chips contains 12 that are good and three that are defective. Three of these chips
are selected, in succession, with replacement, and checked for a defect. Find the probability that the first
chip will be defective, the second defective, and the third good.
19.
A test for a certain disease was given to 2,000 people. Twelve percent were known to have this disease.
For the people who had this disease, the test indicated the presence of the disease in 97% of the people,
was inconclusive for 2.5% , and no disease in 0.5%. For the people who did not have the disease, the test
indicated the presence of the disease in 0.5% of the people, was inconclusive for 0.5%, and indicated no
disease in 99%. A person is chosen at random. What is the probability that the person has the disease,
given that the test indicated that he/she has the disease?
20.
A survey found that 72% of students study for their mathematics final exam and of those who study only
2% fail the exam. Of the student’s who did not study, 83% failed the exam. What is the probability that:
a.
A student studies for the final exam and passes it?
b.
A student will pass the final exam, given he did not study?
c.
A student did study, given that he failed the exam?
21.
On inspecting a lot of 120 pairs of jeans, it was learned that 8 had faulty seams, 5 had improperly sew
zippers, and 2 had both of these defects. If a pair of jeans is selected from this lot, what is the probability
that it will have neither of these flaws?
22.
Consider the following binomial experiment. A heart transplant operation is considered a success if the
patient survives one or more years after the surgery. Suppose the probability that a heart transplant
operation is successful is .57. Of ten patients who have recently undergone such an operation, what is the
probability that one year from now:
a.
none of the heart recipients will be alive?
b.
exactly three will be alive?
c.
at least three will be alive?
d.
all will be alive?
23.
Consider the following game: A pair of dice is rolled. If the sum of the dots on top is 6 or less, your friend
gives you $10. For any other sum, you give your friend $7. What are your expected earnings from this
game?
24.
An insurance company is going to sell one-year life insurance policies with a face value of $50,000 to
25-year-old men for $5500. The company’s mortality tables show that these men will live for one year with a
probability of .9. Consider the company’s earnings from such policies to be values of the random variable.
Find the company’s expected earnings per policy.
25.
A survey of the firms in the Industrial Park revealed the given information about their number of
secretaries.
# of Secretaries
1
2
3
4
Frequency
4
3
5
2
Relative Frequency
a.
Complete the relative frequency column. Give exact answers or round decimal answers to three decimal
places.
b.
What is the mean number of secretaries per firm? Give an exact answer or round a decimal answer to
three decimal places.
c.
If a secretary from these firms is selected at random, what is the probability that he or she works for a firm
with two or more secretaries? Show your work. Give an exact answer or round a decimal answer to
three decimal places.
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FM EC Problems
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26.
Two cards are to be dealt, without replacement from a deck of 52 cards, and the number of kings is to be
recorded.
a.
Find the probability that at least one king will be dealt.
b.
Construct a probability distribution histogram for this experiment.
c.
Find the odds for the hand to contain no king.
27.
For the set of values {12, 14, 17, 17, 23, 13}
Manually find the mean, the median, the mode, and the population standard deviation. When appropriate,
round decimal answers to three decimal places.
28.
Two people bought soft drinks for a party. Maria bought 20 six-packs for $1.79 each, and Bradley bought
15 six-packs for $1.59 each. They sold the drinks for 40 cents per can.
a.
What was the mean purchase price per six-pack?
b.
What was the median price per six-pack?
c.
What was the mean of the two purchase prices?
d.
What was the mean profit per six-pack?
29.
A vegetable manufacturing plant produces canned green beans. Their cans of beans have a mean weight
of 14 oz. with a standard deviation of 0.4 oz and have a normal distribution. What percent of the cans of
beans weigh between 13.5 and 14.5 oz.?
30.
Suppose that the running times for the mile run are normally distributed. The average runner at a local
college runs the mile in 4.5 minutes, with a standard deviation of 0.3 minutes. What is the probability that a
person will run a mile in less than 4 minutes?
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