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Probability

What is probability?

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Thumbtack Experiment

• Consider the following experiment: toss 10 thumbtacks up into the air and let them fall on a flat surface

• How many would you expect to land with the point straight up?

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Thumbtack Experiment

• Lets try the experiment– Toss 5 thumbtacks up and let them

land.– Write down your individual data: how

many landed with the point straight up?

– Group data

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Thumbtack Experiment

• Based on our experiment…What is the probability that a randomly chosen thumbtack that is tossed up will land with the point side straight up?

• Experimental vs. Theoretical• Is there a way to find the theoretical

probability for this experiment?

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Dice Experiment

• Work with your elbow partner– One person rolls 2 dice– One person tallies the sum of the 2

dice

• Record your data on the poster • Histogram

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Dice Experiment

• Based on our experiment…What is the probability that the sum of the 2 dice is– 2?– 5?– 7?– 11?

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Dice Experiment

• Experimental vs. Theoretical• Is there a way to find the

theoretical probabilities for this experiment?

• Equally Likely Outcomes Model– Sample Space of equally likely

outcomes

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Dice Experiment

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Dice Experiment

• Compute (theoretical) probabilities – Compare these results to our

experimental probabilities

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M&M Experiment

• Dump out your bag of M&Ms• Consider the experiment: an M&M

is randomly selected from your pile of M&Ms

• What is the probability of selecting each of the available colors?

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M&M Experiment

• Compare your results with your table group members

• Now compute the probability of selecting each of the available colors for your table group

• Record your group data on the poster

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M&M Experiment

• The theoretical probabilities of obtaining each color from a bag of M&Ms are depicted in the following table: Color Probability

of that color

Yellow 0.14

Red 0.13

Orange 0.20

Brown 0.13

Green 0.16

Blue

What is the probability of blue?

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M&M Experiment

• Make a prediction: How many of each color would be likely to be found in a bag of 50? 100? 250? 500? 1000?