1. The Fair Unfair Polarization
Unit 5 – Probability
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4. How many times would you need to roll a die before you rolled a five?
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5. How many times would you expect to roll a die before you got a five?
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6. Mathematical Probability for a Fair Die
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7. Disclaimer: Neither this activity, nor Mr
***Disclaimer: Neither this activity, nor Mr. Cloud encourages gambling of any sort in any way. Remember this is a “G” rated classroom. All gambling done here is theoretical and only used to help put into context when a problem like this would be necessary to examine. Also, the $100,000,000 mentioned in the activity is 100 million pretend dollars.***
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8. The Fair Dice Game
The situation: You and your partner have a bet. You are going to play a dice game and the winner receives $100,000,000. Each of you will roll one die. Next you will sum the two dice. If the sum is 2, 3, 4, 5, or 6, player 1 wins. If the sum is 7, 8, 9, 10, or 11, player two wins. If 12 is rolled, then the round is a tie and will be rerolled. The first player to win 5 rounds wins the game.
1) Player one for this game is ________________.
2) Player two for this game is ________________.
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9. Does the game seem fair as described above. (Just because Mr
Does the game seem fair as described above? (Just because Mr. Cloud brought it up doesn’t mean it isn’t a fair game…go with your gut instinct) Explain your answer (with more than one sentence).
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10. Play the Game (Best of 9)
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12. 11/15/2018
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13. Possible Outcomes and Probability
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14. What is the probability that, on the first roll, player 1 will win?
Is the dice game Mr. Cloud proposed a fair game? Why or why not?
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15. Your Turn!
Create and describe a dice game very similar to Mr. Cloud’s but would be a fair game. Give a full description and include any reasons why you changed certain rules if they are different from Mr. Cloud’s. Give irrefutable evidence that your game is fair.
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Algebra 1 Institute

16. Complement
If we know the probability that Player A wins, how could you use it to determine the probability that Player B wins without adding the remaining values in the table?
Since one of the two players has to win, the sum of both probabilities -- that of Player A winning and that of Player B winning -- is 1. So a faster way to find the probability that Player B wins is to subtract the probability that Player A wins (12/36) from 1:
1 - (12/36) = (36/36) - (12/36) = 24/36
Player B wins with probability 24/36, or two-thirds of the time.
11/15/2018
Algebra 1 Institute