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Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
Uniform Distributions4.2
Answer Allie's chances of winning are 1/26.
Each briefcase is equally likely to hold the money.
Answer
How would all of this change if she were allowed a second chance after checking the contents of five briefcases?
What are her chances of winning? Is each briefcase equally likely to hold the money? What would you do?
On a TV game show, Allie has the option of taking home $750 or guessing which one of 26 briefcases contains $1 000 000.
Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
Invesgate Uniform Distribuons
Uniform Distributions4.2
1. Create the probability distribution for each experiment.a) the upper face on a single roll of a dieb) the numerical result of a single spin of the spinner shownc) the position a person could be assigned when the eight runners in a race are randomly assigned a starting lane from lanes 1, 2, 3, 4, 5, 6, 7, or 8
3. Compare the three distributions.How are they different? How are they the same?
2. Sketch a probability histogramfor each distribution in step 1.
Click to spin!
Upper face, x Probability, P(x) Value, x Probability, P(x) Lane, x Probability, P(x)
a)
c)
b)
Click here for the solution.
Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
Invesgate Uniform Distribuons
Uniform Distributions4.2
4.Reflect Which distribution(s) from step 1 would be considered a uniform distribution Why?
5. Extend Your Understanding Rewrite the descriptions of the nonuniform examples so they are uniform.
Answer
The die and swimming lane distributions are uniform because every outcome is equally likely.
Answer Part b) could be reworded as "the
resulting section colour of a single spin of the spinner shown" or change the sections to {1, 2, 3, 4, 5, 6, 7, 8}.
Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
Example 1
Uniform Distribuon
Uniform Distributions4.2
A calculator has been programmed to generate a random number between 1 and 5.
a) Classify this distribution.
Random Number, x P(x) x P(x)
Answer
Answer
d) Calculate the expectation. Interpret its meaning.
c) Sketch a graph of the distribution. Comment on the shape of the graph.
b) Calculate the probability distribution.
Answer This is a uniform distribution,
because each number is equally likely.
Answer
Click the window to generate
Clicking the arrow will inject the result(to keep a list of results).
Draganddrop the number into a liston the right before injecting another.
Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
Example 2Fair Game
Uniform Distributions4.2
A game involves drawing a card from a standard deck. A player who draws a heart earns two points. If the player draws a black card, the player loses one point. Is this a fair game?
Click here for the solution.
Hint
Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
Uniform Distributions4.2
Reflect
R1. Is it possible for flipping multiple coins to be a uniform distribution?
R2. What conditions are necessary for a door prize draw to be a uniform distribution?Answer When flipping multiple coins,
having all coins the same is less likely than any other outcome, so it cannot be a uniform distribution.
Every person must have the same number of entries, and thus, the same probability of winning.
Answer
Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
Uniform Distributions4.2
1 True or false?
A uniform distribution can have bars of varying heights.
True
False
FalseAnswer
Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
4.2
B
2 Select the option below which would not be represented by a uniform distribution.
A the top face when rolling a standard die
B the sum of the top faces when rolling a pair of standard dice
C spinning a spinner with four equal sections
D flipping a fair coin
Uniform Distributions
Answer
Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
Uniform Distributions4.2
3 True or false?
The expectation of a uniform distribution must be a decimal.
True
False
FalseAnswer
Unit 04, Lesson 2 4.2 Uniform Distributions.notebook
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April 20, 2018
Uniform Distributions4.2
4 True or false?
The pictured spinner represents a uniform distribution.
True
False
TrueAnswer
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