Being an

**innovative**person to come up for answers to the last question was a challenge. I had to change the game to make sure it becomes fair. Even though I completed this on my own, I still had some help from my peers. They guided me to an answer, while not saying it aloud.

Here is the link to the document.

Analyzing a Game: Before and After...

Step 1: Learn the rules to this game:

rules: each person picks a color, and starts on Orange. Player 1 flips a coin three times and moves his piece to the right for each heads, and to the left for each tails. If the player lands on the color he/she chose in the beginning, he/she wins a point.

Player 2 repeats the process.

Step 2: Discuss with your partner and answer the following questions before playing:

- Do you think that one color is a better choice than the others?

Yes. Every colour except for orange occurs twice, so the probability of getting yellow purple or green is higher than the probability of getting orange.

- Do you think there is a color that you should not pick?

Yes. I think that you should not pick orange, as it has the smallest probability

Step 3: Play the game as a class. Mr. Hancock will play against the whole class.

Step 4: Complete these statements:

- Before playing the game, I thought…

That you could get every colour except for orange.

- Now I think…

That you can only get yellow or purple. It is impossible to get the colours green and orange.

- How is this game connected to positive and negative integers?

This is connected because if you lose a point, then you are subtracting, but when you gain a point you are adding.

PART II

One way to analyze probability, is to count how many distinct possible outcomes there are in a situation.

- How many distinct possible outcomes can you count in Color-Rama?

There are 8 possible outcomes.

There may be more than one way to get certain colors.

A helpful way to count all of the possibilities is to make a tree diagram.

Use this tree diagram to calculate the probability of landing on each color in the game:

- Can you figure out the color for each outcome from this diagram?

- yellow
- purple
- purple
- purple
- purple
- purple
- purple
- yellow

- What is the probability of each of the four colors in the game?

Orange: 1/7

Purple: 2/7

Green: 2/7

Yellow: 2/7

- How could you change the rules to Color-Rama to make it a ‘fair game’ ? (discuss or research what ‘fair game’ really means before you answer?

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