chap. 6 sec. 1 presentation

8/14/2019 Chap. 6 Sec. 1 Presentation

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Probability SimulationChapter 6 Section 1


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3 methods to answer questions ofprobability1. Try to estimate the likelihood of a result of interest

by actually observing the random phenomenon

many times and calculating the relative frequencyof the results (Empirical

Do IT!)2. Develop a mathematical probability model and use

it to calculate a probability (TheoreticalThinkabout IT!)

3. Start with a model, in some fashion, that reflectsthe truth about the random phenomenon anddevelop a plan for imitating a number ofrepetitions of the procedure (SimulationFakeIT!)


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Simulations BIG & small!

BIG! Example 6.1

Virtual-Reality applications for training military Using simulators to train pilots & drivers

small Example 6.2

Using the flip of a coin to simulate boys/girls born ina family

NOTE: The AP Exam gives full credit forproblems solved by simulation even if the

problem doesnt call for it!


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Simulation Tools

Random Digits Table

Table Bvery back

Each digit has an equal chance of appearing

Each group of digits has an equal chance ofappearing

Calculator-randInt command math > prb > randInt > input (min, max, # of trials)

You can store values in a List for use

STO > List name


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Assigning Digits for Simulation Choose a person at random from a group of

which 70% are employed.

Choose a person at random from a group ofwhich 73% are employed.

Choose one person at random from a group ofwhich 50% are employed, 20% are unemployed,and 30% are not in the labor force.


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Simulation Steps:A couple plans to have children until they have a girl or until

they have four children, whichever comes first. What is the

probability that they have a girl?

1. State the problem or random phenomenon.

2. State the assumptions. Probabilities/Relative Frequencies Independent/Dependent

When do you stop?

3. Assign digits to represent outcomes.

4. Simulate many repetitions

5. State your conclusions. What did you find?


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Pg. 397 6.1-6.5 odd

Pg. 402 6.8, 6.12Homework Assignment


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Simulation Steps:Orders of frozen yogurt flavors (based on sales) have the

following relative frequencies: 38% chocolate, 42% vanilla, and20% strawberry. We want to simulate 10 customers entering

the store and ordering yogurt.

1. State the problem or random phenomenon.

2. State the assumptions. Probabilities/Relative Frequencies

Independent/Dependent

When do you stop?

3. Assign digits to represent outcomes.4. Simulate many repetitions

5. State your conclusions. What did you find?


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LETS PLAY PLINKO!Probability Simulation


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Think this through!

What position(s), one through nine, do youbelieve would be the worst to start your chip in?

Why?

What position(s), one through nine, do youbelieve would be the worst to start your chip in?

Why? LETs SIMULATE!

What do we need to assume?

Set-up the simulation!


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Grade Distribution

1 2 3 4 5 6 7 8 9

A

B

C

DF


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chap. 6 sec. 1 presentation

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