Foundations of Algebra and Geometry
Chapter 7, 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:
g. Is Bul a game of skill, chance, or both? Explain.
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?
b. What is the probability that a U.S. school bus is headquartered in New Jersey?
c. What is the probability that an accident in New Mexico involved collision with another vehicle or with a fixed object?
d. What is the probability that a student riding a bus in the United States lives in New Hampshire?
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.
c. Based on your results, what is the probability that Kate will enjoy clear skies on at least three days of her vacation?