section 6.1.1 the idea of probability statistics
TRANSCRIPT
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.”
AP Statistics, Section 6.1, Part 1 4
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
AP Statistics, Section 6.1, Part 1 6
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.
AP Statistics, Section 6.1, Part 1 7
SimulationsSimulationsCory rolls a die 30 times.How often does a number of 2 or
less appear?
AP Statistics, Section 6.1, Part 1 8
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?
AP Statistics, Section 6.1, Part 1 12
300 Trials300 Trials
With 300 “rolls”, Emil got a number less than two, 90 times (30%).
What was expected?
AP Statistics, Section 6.1, Part 1 13
Simulating tossing multiple Simulating tossing multiple coinscoins
AP Statistics, Section 6.1, Part 1 14
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