1.	A spinner with regions numbered 1 to 4 is spun and a coin is tossed.  Both the number spun and whether the coin lands heads or tails is recorded.  Write the sample space. 	

2.	Three coins are flipped simultaneously and it is recorded whether each coin lands heads or tails.  List the sample space. 	

3.	A pair of dice is rolled.  Sam says there are 36 outcomes in the sample space for this procedure and Sally says there are 11 outcomes in the sample space.  Explain how they could both be correct. 	

4.	Exactly one of three contestants will win a game show.  The probability that Terry wins is 0.25 and the probability that Chris wins is 0.65.  What is the probability that Toni wins? 	

5.	If the probability that Kerry gets an "A" in English class is 0.82, what is the probability that Kerry does not get an "A"? 	

6.	Suppose three fair coins are tossed and the number of heads that appear is recorded.  What is the probability of getting exactly two heads? 	

7.	A pair of fair dice is rolled and the sum of the faces showing is recorded.  What is the probability of getting a sum greater than nine? 	

8.	We wish to make a spinner that will be numbered 1 to 4, but will have the probability of spinning a "1" be 0.5.  Draw the face for such a spinner. 	

9.	Find the probability of drawing a three or a heart from a regular (bridge) deck of cards.  (Such a deck consists of four suits of 13 cards each.  The suits are hearts, spades, diamonds, and clubs.  The cards are 1 through 10, Jack, Queen, and King.) 	

10.	We must create a license plate code that consists of two letters followed by three digits.  The letters cannot repeat, but the digits may.  How many such license plate codes can be formed? 	

11.	A pizza can be made with any of the following toppings:  cheese, pepperoni, sausage, mushrooms, anchovies, green peppers, or olives.  How many different three-topping pizzas can be made?  Doubling of any topping is not allowed. 	

12.	A license plate code consists of two letters followed by three digits.  The letters cannot repeat, but the digits can.  What is the probability that a randomly chosen plate has all three digits the same? 	

13.	A pizza can be made with any of the following toppings:  Cheese, pepperoni, sausage, mushrooms, anchovies, green peppers, or olives.  Doubling of any topping is not allowed.  What is the probability that a randomly created three-topping pizza will contain mushrooms? 	

14.	A student is taking a five-question True/False test.  If the students chooses answers at random, what is the probability of getting all questions correct? 	

15.	Below is a probability model for the number of automobiles owned by a randomly chosen family in a large town.  What is the mean number of automobiles owned?

Number of automobiles	
0	
1	
2	
3	

Probability	

0.15	

0.20	

0.55	

0.10	

16.	Suppose a game has four outcomes, A, B, C, and D. The probability of outcome A is 0.4, the probabilities of each of the other outcomes is 0.2.  A player receives $2 if outcome A occurs, $3 if outcome B occurs, $1 if outcome C occurs, and must pay $5 if outcome D occurs.  What is the mean value of one trial of this game? 	

17.	The mean value of one trial of a carnival game is –$.05.  Explain what this means. 	

18.	Suppose a trial consists of rolling a single die and reporting the number that is rolled.  What are the possible outcomes?  Are they equally likely?	

19.	Suppose a trial consists of rolling two dice and reporting the sum of the numbers rolled.  What are the possible outcomes?  Are they equally likely?	

20.	Suppose a trial consists of rolling two dice and and reporting the smaller of the two numbers rolled?  What are the possible outcomes?  Are they equally likely?	

21.	The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 lbs., with a standard deviation of 0.35 lbs.  The distribution of weights is approximately normal.  What is the probability that one potato chosen at random will weigh more than 1.65 lbs.? 	

22.	The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 lbs., with a standard deviation of 0.35 lbs.  The distribution of weights is approximately normal.  What fraction of the potatoes in the shipment will weigh between 0.25 and 2.35 lbs.? 	

23.	In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm.  Between what two measurements will 95% of all diameters of ball bearings be found? 	

24.	In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm.  Each hour a sample of 20 bearings is drawn, measured, and the mean diameter of the sample found.  What is the standard deviation sx of the sample mean? 	

25.	A publisher wishes to know what percent of book pages will need graphics editing.  A random sample of 25 pages in a textbook finds that 58% of the pages had drawings or figures on them.  The standard deviation for this percent is 9.9%.  If the publisher wishes to reduce the standard deviation to 3.3%, how many pages should the publisher sample? 	

26.	A game consists of tossing a coin and rolling a six-sided die. The results can be recorded easily; for example, if heads shows on the coin and a 4 shows on the die, record this as H4. List the sample space for the results of this game. 	

27.	A game consists of tossing three coins. Find the probability model for the number of coins showing heads. 	

28.	A football stadium snack bar conducted a survey and found that 30 customers bought one item, 52 customers bought two items, 21 customers bought three items, and 12 customers bought four items. What is the mean number of items purchased per customer? Round your answer to the nearest tenth. 	

29.	Suppose you use a spinner to choose a random number between 0 and 1.  Which is more likely:  Choosing a number between 1/3 and 2/3, or between 1/2 and 3/4? 	

30.	According to the Central Limit Theorem, how does the variance of averages over four observations compare to the variance of individual observations?	

Answer Key

1.	{(1,H), (2,H), (3,H), (4,H), (1,T), (2,T), (3,T), (4,T)}	
2.	{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}	
3.	Sam counts 36 outcomes in the sample space by observing the number rolled on each die.  Sally counts 11 outcomes by observing the sum rolled on the die.	
4.	The probability Toni wins is 0.1.	
5.	The probability Kerry does not get an A is 0.18.	
6.	The probability of getting exactly two heads is 3/8 or 0.375.	
7.	The probability of rolling a sum greater than nine is 6/36 or 0.167.	
8.	Answers may vary.  Any spinner face that shows half the face labeled "1" is correct.	
9.	The probability of drawing a three or a heart is 16/52 or 0.308.	
10.	650,000	
11.	210	
12.	6500/650,000 = 1/100 = 0.01	
13.	30/210 = 1/7 = 0.143	
14.	1/32 = 0.03125	
15.	The mean number of automobiles owned is 1.6.	
16.	The mean value of one trial is $0.60.	
17.	The mean value gives the win or loss after a very large number of trials.  In this case, a player would lose an average of 5 cents for each trial.	
18.	Possible outcomes are 1, 2, 3, 4, 5, 6.  They are equally likely.	
19.	Possible outcomes are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.  They are not equally likely.	
20.	Possible outcomes are 1, 2, 3, 4, 5, 6.  They are not equally likely.	
21.	0.16	
22.	99.7%	
23.	95% of all diameters will be between 4.996 and 5.004 mm.	
24.	0.000447	
25.	225 pages	
26.	H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6	
27.	Number of heads	
0	
1	
2	
3	

Probability	
1/8 or .125	
3/8 or .375	
3/8 or .375	
1/8 or .125	

28.	2.1 items	
29.	Choosing a number between 1/3 and 2/3.	
30.	The variance of the averages is half that of the individual observations.