Foundations of Algebra and Geometry
Chapter 7 Answers
Probability and Decision Making
Probability can be applied to phenomena as old as playing an ancient game of chance, as common as riding a bus to school, and as recent as yesterday's weather.
Part A, Games in Other Cultures
1. The Mayan game of Bul is a game of chance.
a. Read the rules of the Mayan game of Bul. Note that in Paragraph 3, the comment in parentheses should read "1 burned side and 3 unburned = 1, etc."
b. Choose "Play Bul" to play the game. The computer will throw the corn and move the players each time you click on (TOSS THE CORN). After you understand the rules, choose "Play Bul Faster" for a quicker game.
Sketch the game board after each move:
Answers for c-f
g. Is Bul a game of skill, chance, or both? Explain.
[Chance. Each move depends on the throw of the corn. Therefore, a player has no control over the outcome of the game and wins only by being luckier than the other player.]
Part C, Theoretical Probability
2. Answer the questions below about School bus accidents.
a. What is the probability that a person injured was not a pupil?
[6/19]b. What is the probability that a U.S. school bus is headquartered in New Jersey?
[3/80]c. What is the probability that an accident in New Mexico involved collision with another vehicle or with a fixed object?
[139/146]d. What is the probability that a student riding a bus in the United States lives in New Hampshire?
[71/12,250]e. The comments preceding the statistics include this statement: "Approximately 7 out of 10 accidents involved property damage with no injuries." How was that conclusion reached?
Part E, Making Connections
3. Kate is planning a 7-day February ski vacation near Salt Lake City, Utah. She wants to predict the probability that she'll enjoy clear skies on at least 3 days of her vacation.
a. Find the mean number of February days with Clear skies for Salt Lake City. (The first number in each row gives the number of years represented by data in the table. Following are mean numbers of "Clear, Cloudy, Partly Cloudy" days for each month). Write the percent of February days with clear skies rounded to two digits.
4. You can use pairs of digits in a random number table to represent
percents from 0 to 99:
Find the 14-digit sequence 570 42194 49043 2 in row 7 of the Random number table.
a. Let the digits represent the seven days during which Kate is in Salt Lake City. Let any pair of digits less than or equal to the percent in 3a represent a clear day. How many clear days are represented by the digits?
b. Continue with the next 19 sets of 14 digits. For each set, find the number of clear days represented by the digits.
[1, 1, 2, 1, 3, 2, 1, 0, 0, 0, 2, 1, 2, 2, 1, 3, 0, 0, 1]c. Based on your results, what is the probability that Kate will enjoy clear skies on at least three days of her vacation?
[There are 3 or more clear days in 2 of the 20 simulations.
2/20 = 10%]
Games and sports generate huge amounts of data. For that reason, they lead naturally to questions about probability.
Part C, Choosing a Group
1. Baseball, football, and basketball are familiar to most Americans. But what about cricket, elephant polo, and danball?
a. Read Law 1 of the Rules of cricket. How many ways are there to choose a captain and deputy from a cricket team?
[110 ways]b. If the Screwey Tuskers are one of the top three Elephant polo teams, how many ways are there to choose the other two top teams?
[Choose 2 teams from a group of 7; 21 ways]c. You have a total of 6 players on your Danball team. How many ways can you choose a starting team?
[Choose 3 players from a group of 6; 20 ways]
Part E, Making Connections
2. Find the statistics for the 1995 Baltimore Orioles baseball team.
a. "AVG" is the average number of base hits a player each time he came to bat. In a randomly chosen at-bat, what is the probability that Hoiles got a hit?
[0.25]b. "SB" is the number of times a player stole a base successfully. "CS" is the number of times the player was unsuccessful at stealing a base. When Bass attempted to steal a base, what were the odds that he would succeed?
[100%]c. What were the odds against Zaun getting a base hit?
[740 to 260, or 37 to 13]d. When pitcher Lee won (W) or lost (L) a game, what was the probability that he won?
[1 or 100%]e. "ERA" is the average number of runs that a pitcher allows for every 9 innings he pitches. How many runs would you expect Harris to allows in 36 innings? in 60 innings?
[18 runs; 30 runs]