Section 6.1.1 The Idea of Probability

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Section 6.1.1 The Idea of Probability. AP Statistics www.toddfadoir.com/apstats. 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.

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### Section 6.1.1The Idea of Probability

AP Statistics

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

Random is not “haphazard”
• The Big Idea: “Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run.”

AP Statistics, Section 6.1, Part 1

Definition of Random
• We 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

Definition of Probability
• The 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 allow us to see those long-term frequencies

AP Statistics, Section 6.1, Part 1

Independence
• In 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.

AP Statistics, Section 6.1, Part 1

Simulations
• Cory rolls a die 30 times.
• How often does a number of 2 or less appear?

AP Statistics, Section 6.1, Part 1

Create the random numbers

AP Statistics, Section 6.1, Part 1

Categorize the results

AP Statistics, Section 6.1, Part 1

Count the results

AP Statistics, Section 6.1, Part 1

Consider
• During 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?

AP Statistics, Section 6.1, Part 1

300 Trials
• With 300 “rolls”, Emil got a number less than two, 90 times (30%).
• What was expected?

AP Statistics, Section 6.1, Part 1

Simulating tossing multiple coins

AP Statistics, Section 6.1, Part 1

What about things you can’t “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

Assignment
• Exercises: 6.1, 6.3, 6.5, 6.7, 6.10

AP Statistics, Section 6.1, Part 1