Games of Chance

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Games of Chance
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Todays Learning Goals

• We will continue to think about the link between
  fractions, decimals, and percents.
• We will begin to develop a deep understanding of
  experimental and theoretical probabilities and
  the relationship between them.
• We will determine ways of finding experimental
  probabilities.
• We will begin to develop an understanding of
  determining when a game is fair or not.
• We will begin to develop the ideas of equally
  likely and non-equally likely outcomes.

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Whats in the Bag?

• Today, we are going to conduct an experiment. In
  front of the class, I have a mysterious bag. The
  bag contains blue, yellow, and red blocks.
  However, I am not going to show you how many of
  each color are in the bag. They might be all one
  color or there might be some of each color.

• What could we do to help us predict how many
  blocks of each color are in the bag without
  emptying the bag and counting the blocks?

Nicewe could take a sample of blocks and use the
sample to come up with an estimate.
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Whats in the Bag?

• Each person will randomly select one block at a
  time from the bag.

• Each of you will record the results in the table
  on the worksheet.

• After each draw, we will return the block to the
  bag and shake the bag before the next student
  selects another block.

• Why do you think we shake the bag?

Greatso that the block chosen is chosen at
random.
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Whats in the Bag?

• After the first sample, what do you think is in
  the bag?

Goodbased on the sample only, you would guess
that the bag was 100 of the color you pulled.

• How could we get a better idea of what is in the
  bag?

Yestake more samples.

• After each sample, determine the percentage of
  blocks that are red/yellow/blue in the bag.

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Whats in the Bag?

• The percentages we found after each sample are
  called experimental probabilities because it is
  the probability of pulling that color based on
  the experimental data.

• After 25 samples, dump out the contents of the
  bag. Count the number of reds, yellows, and
  blues in the bag. What is the percentage of red
  in the bag?

Good50 because there were 50 red out of 100
blocks.

• This is called the theoretical probability of
  pulling a red from the bag because it is the
  actual chance not based on experimental data, but
  by actual amounts.

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Whats in the Bag?

• What is the theoretical probability of pulling a
  yellow?

Correct25 because there were 25 yellow out of
100 blocks.

• What is the theoretical probability of pulling a
  blue?

Good25 because there were 25 blue out of 100
blocks.

• What is the difference between experimental
  probability and theoretical probability?

Greatexperimental probabilities can change
depending on the data that was collected.
Theoretical probabilities are based off of the
actual amounts so they cannot change.
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Whats in the Bag?

• Was each block equally likely to be selected from
  the bag? Explain why or why not.

Yesbecause each block was the same size and the
bag was shaken up.

• Was each color equally likely to be selected from
  the bag? Explain why or why not.

Nobecause there were different amounts of each
color in the bag.

• What is the probability of drawing a white block
  from the bag?

Great0 because there were zero white blocks in
the bag.
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Matching Colors

• April and Tioko invented a two-player spinner
  game called Match/No-Match.

• A player spins this spinner twice on his or her
  turn.

• If both spins land on the same color (a match),
  Player A scores. If the two spins land on
  different colors (a no-match), Player B scores.

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Matching Colors

• April and Tioko thought that there were two
  matching combinations (blue/blue and
  yellow/yellow) making Player A twice as likely to
  get a chance at getting a point. Player B only
  gets points if the colors do not match! So,they
  decided that Player A should score only 1 point
  for a match and Player B should score 2 points
  for a no-match.

• We can simulate a spinner with just two colors on
  our graphing calculators. Press the APPS button.
  Go down to the Prob Sim application and press
  ENTER.

• Once in the Prob Sim application, select Spin
  Spinner. Then hit the ZOOM button on your
  calculator which corresponds to the SET button
  within the screen.

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Matching Colors

• Under Sections, type in 2 so that the spinner has
  only two sections.

• Hit the GRAPH button which corresponds to the OK
  button in the screen.

• Lets assign 1 Blue section and
• 2 Yellow Section.

• Hit the WINDOW button to spin the spinner 1 time.
  

• Play the Match/No-Match game with a partner.
  Take a total of 24 turns (12 turns for each
  player). For each turn, record the color pair
  and award the appropriate points to the
  appropriate player.

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Partner Work

• You have 20 minutes to work on the following
  problems with your partner.

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For those that finish early

• 1. Suppose that a bag had 15 blues, 20 reds,
  and 11 yellows. How many reds would have to be
  added so that the probability of drawing a red
  block is ½.
• 2. Are a match and a no-match equally likely?
  Explain your reasoning.
• 3. In 100 turns of the Match/No-Match game, how
  many times would you expect each of the following
  to occur?
• a) two yellows b) two blues
• c) one yellow and one blue d) at least one
  yellow

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Big Idea from Todays Lesson

• Experimental probabilities can change depending
  on the number of samples/size of the sample.
• Theoretical probabilities are determined from
  figuring the chance of something happening from
  actual amounts.
• A game is fair if all members have an equally
  likely chance of getting points and they get the
  same amount of points for each chance.

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Homework

• Complete Homework Worksheet