Title
Three Strikes and You're Out (Dorothy Gieck)
Goals
Students will work with the concept of probability. Students will work in small groups in order to arrive at a method for calculating the probability of winning a game where blocks are pulled out of a bag. They will be able to explain, and justify, how they arrived at this method to the rest of the class.
Abstract
This activity, which is set in the context of the game from the "The Price is Right" television show, deals with the probability of winning the game. Students are asked to form small groups to discuss the problem and come to a method for finding the probability of winning this game. This activity could be used with a probability unit.
Problem Statement
Most people have watched the game show, "The Price is Right." One of the games that is played to win a car is the "Three Strikes and You're out" game. In the game four blocks with numbers on them and three blocks with strikes on them are put into a bag. The player selects a block. If the block is a number, the player chooses a position in the amount of the price of a car that he thinks is correct. If he is correct, the number is place in the proper position and he selects another number. If he is incorrect, the number goes back into the bag. If the player pulls out a strike block, record is taken. Players continue to draw blocks until they have found the correct price or they have selected the three strikes and they are out of the game.
We will simplify the game to eliminate the part about the position of the number. You will be a winner if you choose the four number blocks before you choose the three strikes. Come up with a probability for winning the game and analyze these probabilities.
Instructor Suggestions
1. Set the stage by discussing the "Problem Statement" (see above) with your students.
2. Distribute the "Three Strikes and You're Out?" activity sheet and allow the students to individually read the activity.
3. Have the students form small-groups and complete the questions on the activity sheet.
4. When the small groups are finished, have a spokesperson for each group share the group answers for specific parts of the activity and explain their method and reasoning involved in arriving at their probability.
5. Discuss the students work as it relates to probability.
Materials
"Three Strikes and You're Out" activity sheet, blocks and bags for each group
Time
Introduction of Problem Statement (5 min.), small group work (20 min.), presentation of small group work and large group discussion (15 min.), extension questions (5 min.)
Mathematics Concepts
Discrete Mathematics Concepts:
Counting Techniques, Probability
Related Mathematics Concepts:
Combinations, Permutations, Probability
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Mathematics
Colorado Model Content Standards Addressed
Algebraic Techniques (2), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be adapted to many levels of mathematics. It could be integrated into any class that is studying probability. I would use it to help review or reinforce concepts that had already been introduced with probability.
Further Investigation
Discussion of the expectation of the "house". Does the position of the numbers make a significant difference?
Variations/Comments
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W. H. Freeman and Company.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
Colorado Model Content Standards for Mathematics (1995)
CBS, The Price is Right