MATH HONORS 2: Game Theory Assignment
You will be working with a partner in this assignment, so the two of you only need to submit a total of one copy of your
collaborative work. For this assignment, you will take on the roles of Educational Consultants for a city’s board of
education. The mathematics curriculum in your district is being over-hauled, and one of the directives is to teach
probability to Grade 10 students through the context of a game. Your task is to write a report that provides evidence of
various types of probability and combinatoric situations that are expected to be covered during the academic year
which occur in any one of the following ten games:
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Backgammon (two dice and board pieces)
Yahtzee (five dice)
Farkle (five dice)
Risk (five dice and board pieces)
Mastermind (colored pegs)
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Blackjack (one deck of cards)
Hearts (one deck of cards)
Hold ‘Em Poker (one deck of cards)
UNO (one special deck of cards)
Scrabble (bag full of letters and board)
After playing the game for a while, you and your partner will notice that there are some situations that occur quite
frequently. Due to the random nature of the game (the rolling of dice or the drawing of shuffled cards or mixed up letters),
it is useful to be able to calculate the number of different outcomes that can occur in these common situations, as well as
the probabilities of these different outcomes, in order to develop winning strategies.
Part 1
Write an explanation of the situation in the game, the calculation required to determine an answer, and an evaluation of
whether it is an example of an appropriate Grade 10 level for ALL of the following SIX concepts:
1. Calculating a simple probability
2. Calculating the probability of the complement of an event
3. Representing a multi-dimensional sample space
4. Calculating the probability of a combined event (using “or” AND “and)
5. Recognizing and applying mutually exclusive events (using “or” OR “and”)
6. Recognizing and applying independent events (using “and” OR “given that”)
Part 2
Write an explanation of the situation in the game, the calculation required to determine an answer, and an evaluation of
whether it is an example of an appropriate Grade 10 level for ANY SIX of the following eight concepts:
1.
2.
3.
4.
5.
6.
7.
8.
Representing probabilities of two events using a Venn diagram
Calculating the probability of a conditional event using a reduced sample space on a Venn diagram
Calculating the probability of a conditional event using a tree diagram (given the first event)
Calculating the probability of a conditional event using a tree diagram (given the second event)
Calculating a permutation
Calculating a permutation with identical objects
Calculating a permutation involving groupings of objects
Calculating a combination
Part 3
Conclude your report by writing a recommendation as to whether the game that you and your partner studied would be a
successful choice in teaching the concepts of probability and combinatorics in a Grade 10 math course.