Mathematics I / Review
Unit 4 – Chance of Winning / Name:

MM1D1. Students will determine the number of outcomes related to a given event.

a.  Apply the addition and multiplication principles of counting.

1. / Tom is going to dinner at a pasta restaurant. He is allowed to choose one of three pastas, one of 4 sauces, and one of three meats. How many different pasta dishes can he make?
2. / Slips of paper labeled 0, 2, 4, 5, and 6 are placed in a hat. Two slips are drawn at the same time. How many different possibilities are there for the PRODUCT of the numbers on the two slips?

MM1D1. Students will determine the number of outcomes related to a given event.

b. Calculate and use simple permutations and combinations.

3. / Our club elections are tomorrow. How many different ways can president, vice president, secretary and treasurer been chosen from 8 students?
4. / Your math club is going on a trip to Six Flags. Although the club has 15 members it can only afford to send 6 members. How many different combinations can be formed?

MM1D2. Students will use the basic laws of probability.

5. / If you were to draw a card from a standard deck, what is the probability of drawing a diamond?

MM1D2. Students will use the basic laws of probability.

a.  Find the probabilities of mutually exclusive events.

Use the following information for # 6-7:

The governors of three states appoint a crime commission that includes members as shown.
Florida / Alabama / Georgia / Total
Male / 4 / 3 / 3 / 10
Female / 8 / 6 / 7 / 21
Total / 12 / 9 / 10 / 31
6. / If the chairperson is randomly selected, find the probability of getting a man or a Floridian.
7. / At each meeting, one of the members is randomly chosen to be secretary. Find the probability that the first two secretaries are both men if the same person cannot be chosen 2 weeks in a row.
8. / Bella has a deck of 52 cards. If Bella picks one card from the deck without looking, what is the probability that she will either choose a club or a spade?

MM1D2. Students will use the basic laws of probability.

b.  Find the probabilities of dependent events.

9. / In a class of 8 boys and 9 girls what is the probability of choosing a girl and then a boy for a team?
10. / Given a standard deck of 52 cards, find the probability of drawing 2 clubs.
11. / A box of parts contains 8 good items and 2 defective items. If 2 are selected at random with replacement, find the probability that one is defective and the other is not.
12. / Two dice are rolled and the sum is recorded. Which of the following events has a probability equal to 1?
(A) sum = 3 or 4 (B) sum > 7 (C) sum = 13 (D) sum < 13
13. / A box of parts contains 8 good items and 2 defective items. If 2 are selected at random withOUT replacement, find the probability that one is defective and the other is not.

MM1D2. Students will use the basic laws of probability.

c.  Calculate conditional probabilities.

14. / Given a bag of 3 red marbles, 5 blue marbles and 4 green marbles, find the probability of drawing a red marble given that one red marble has been chosen.

Use the following information for # 15-16:

The following table represents a sample of 200 drivers stopped for speeding.

Number of mph
over speed limit
5-10 / >10 / Total
Wearing
Seatbelt / Yes / 42 / 123 / 165
No / 8 / 27 / 35
Total / 50 / 150 / 200
15. / From the table, what is the probability that a person stopped for speeding was not wearing a seatbelt given that they were traveling 5 to 10 mph over the speed limit?
16. / What is the probability that a person stopped for speeding was traveling more than 10 mph over the speed limit or was not wearing a seatbelt?

MM1D2. Students will use the basic laws of probability.

d.  Use expected value to predict outcomes.

17. / Find the expected value of the following event.
E / P(E)
1 / .25
2 / .30
3 / .10
4 / .35
18. / Joe used a spinner with 10 equal sections. The sections of the spinner contained the following numbers. What is his expected value?
4, 2, 6, 8, 3, 7, 8, 2, 2, 1
19. / Marietta has a nail gun that malfunctions 15% of the time. If she uses the nail gun 80 times in the next 2 weeks, how many times can she expect it to malfunction? Round your answer to the nearest whole number.
20. / The Thompson Construction Company is considering bidding on a job to construct a building. If the bid is won, there is a .7 probability of making a $175,000 profit and there is a probability of .3 that the contractor will lose $20,000.
a. / What is the expected value for this bid?
b. / Should the bid be submitted? Explain your answer. {No right or wrong answer, just SUPPORT your answer with an appropriate explanation!}

MM1D3. Students will relate samples to a population.

a.  Compare summary statistics (mean, median, quartiles, and interquartile range) from

one sample data distribution to another sample data distribution in describing center

and variability of the data distributions.

21. / Given the following data sets, find the set with the most variability.
Set 1 / Set 2 / Set 3 / Set 4
Mean / 45 / 50 / 50 / 60
Q1 / 30 / 20 / 30 / 50
Median / 45 / 40 / 45 / 65
Q3 / 60 / 60 / 65 / 95
22. / The following boxplots show the number of cookies eaten by students in our class. The top boxplot represents the cookies eaten by the boys and the bottom boxplot represents the cookies eaten by the girls. Based on the boxplots, which of the following statements about the cookies eaten is incorrect?
(A) / About half of the boys ate more cookies than any of the girls. /
(B) / All of the boys ate at least one cookie.
(C) / Half of the girls ate 2 or more cookies.
(D) / ¾ of the girls ate 3 or fewer cookies.

MM1D3. Students will relate samples to a population.

b.  Compare the averages of the summary statistics from a large number of samples to

the corresponding population parameters.

23. / Several taste tests were conducted across the country to determine the consumer ratings of a new sugar-free ice cream. Consumers were asked to rate the level of sweetness on a scale of 1 to 10, with 10 being extremely sweet. The mean ratings in these samples were:
2 / 2 / 4 / 4 / 4 / 5 / 5
6 / 6 / 6 / 7 / 7 / 7 / 7
7 / 7 / 8 / 8 / 9 / 9
Find the mean, median, and mode (optional: MAD and IQR). What can you conclude about how all consumers will feel about the level of sweetness in this new product? Explain.

MM1D3. Students will relate samples to a population.

c.  Understand that a random sample is used to improve the chance of selecting a

representative sample.

24. / Which of the following would be a simple random sample?
(A) / Choosing all residents in a single block that has been randomly chosen.
(B) / Putting one number in a hat for each participant and then drawing one number.
(C) / Separating boys and girls into two groups and then choosing one from each group.
(D) / Sending questionnaires and waiting for responses.

MM1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

25. / Find the mean and the mean absolute deviation of the following data set.
10 / 13 / 43 / 32 / 17
19 / 25 / 25 / 23 / 15