Friday, October 03, 2014

The Rainbow Revealed

For math, we recently completed a document all about probability. I did this with the members of my table.

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:

  1. 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.

  1. 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:

  1. Before playing the game, I thought…
That you could get every colour except for orange.

  1. Now I think…
That you can only get yellow or purple. It is impossible to get the colours green and orange.

  1. 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.


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

  1. 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:
  1. Can you figure out the color for each outcome from this diagram?
  1. yellow
  2. purple
  3. purple
  4. purple
  5. purple
  6. purple
  7. purple
  8. yellow
  1. 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
  1. 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?
Flip the coin 2 times, take-away one of the yellow’s, and then make orange just a tile.

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