7th Grade Math

Lesson 3D Predictions 467

In a number-cube game, players

roll two number cubes. Play this

game with a partner.

Player 1 rolls the number cubes. Player 1 wins if the total of the

numbers rolled is 5 or if a 5 is shown on one or both number

cubes. Otherwise, Player 2 wins. Record the results in a table

like the one shown below.

Game

1

2

Player 1 Player 2

Player 2 then rolls the number cubes and the results are

recorded.

Continue alternating the rolls until each player has rolled the

number cubes 10 times.

the Results

9. Make an organized list of all the possible outcomes resulting from one roll.


10. Calculate the theoretical probability of each player winning and the
    experimental probability of each player winning. Write each probability as
    a fraction and as a percent. Then compare these probabilities.


11. MAKE A CONJECTURE Based on the theoretical and experimental probabilities
    of each player winning, is this a fair or unfair game? Explain your reasoning.


12. E WRITE MATH If the game is fair, explain how you could change the
    game so that it is unfair. If the game is unfair, explain how you could
    change the game to make it fair. Explain.


13. Compare the probabilities in Exercises 2 and 4.


14. GRAPH THE DATA Make a coordinate graph of the experimental probabilities
    of Player 1 winning for 5, 10, 15, and 20 games. Graph the ordered pairs
    (games played, Player 1 wins) using a blue pencil, pen, or marker. Describe
    how the points appear on your graph.


15. Add to the graph you created in Exercise 6 the theoretical probabilities of
    Player 1 winning for 5, 10, 15, and 20 games. Graph the ordered pairs
    (games played, Player 1 wins) using a red pencil, pen, or marker. Connect
    these red points and describe how they appear on your graph.


16. MAKE A PREDICTION Predict the number of times Player 1 would win if the
    game were played 100 times. Is this a fair or unfair game? Explain.

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