Section 6.1.1 The Idea of Probability Statistics.

Section 6.1.1Section 6.1.1The Idea of ProbabilityThe Idea of ProbabilityStatistics

Probability is studied…Probability is studied…When looking at games of

chance ◦cards, dice, lotteries

When looking at social science data◦Life, death

When looking at scientific data◦Variations in individual measurement

are random

AP Statistics, Section 6.1, Part 1 2

The idea of probabilityThe idea of probabilityTo understand why we can trust

random samples and randomized comparative experiments, we must look closely at chance behavior.

AP Statistics, Section 6.1, Part 1 3

Random is not Random is not “haphazard”“haphazard”The Big Idea: “Chance behavior is

unpredictable in the short run but has a regular and predictable pattern in the long run.”

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Definition of RandomDefinition of RandomWe call a phenomenon random

if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions.

AP Statistics, Section 6.1, Part 1 5

Definition of ProbabilityDefinition of ProbabilityThe probability of any outcome

of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions. That is, probability is long-term frequency.

Computer simulations can allows us to see those long-term frequencies

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IndependenceIndependenceIn order for an event to be

considered random, it must be independent.

That is, it must not be influenced by other (perhaps previous) events.

Example:◦Flipping a head does not make it

more probable that a tail will occur next.

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SimulationsSimulationsCory rolls a die 30 times.How often does a number of 2 or

less appear?

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Create the random Create the random numbersnumbers

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Categorize the resultsCategorize the results

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Count the resultsCount the results

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ConsiderConsiderDuring the last simulation, Cory

“rolled” numbers two or less 11 times. (36.7%)

Is this what you expected?Why wasn’t it exactly 10.What would happen if Cory

“rolled” 300 times?

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300 Trials300 Trials

With 300 “rolls”, Emil got a number less than two, 90 times (30%).

What was expected?

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Simulating tossing multiple Simulating tossing multiple coinscoins

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What about things you can’t What about things you can’t “simulate”“simulate”Spin a penny on your desk.

◦How many times does it fall heads up?

◦What is the probability that it fall heads up?

Toss a thumbtack on a hard surface 100 times. ◦How times did it lands point up? ◦What is the probability that it lands

point up?AP Statistics, Section 6.1, Part 1 15

AssignmentAssignmentExercises: 6.1 - 6.7

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