Test 2 Notes
5.1 How can probability quantify randomness?
•
Probability gives us the foundation necessary to make inferences about the population of
interest based on the information obtained from sample data.
•
Probability of an event
: the proportion of times the event is expected to occur in many
repeated trials of a random phenomenon;
p(event)
o
chance behavior is unpredictable in the short run but has a regular and predictable
pattern in the long run
o
probability describes only what happens in the long run
o
probability=longterm RF
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the law of large numbers
: as the number of repetitions of a random phenomenon
increases, the proportion with which a certain outcome is observed gets closer to the
probability of the outcome
o
it gets closer and closer to 50% the longer the study
•
independent trials: different trials of a random phenomenon are independent if the
outcome of any one trial is not affected by the outcome of any other trial
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Ex 5.6: consider a random number generator designed for equally likely outcomes. Which
of the following is not correct, and why?
o
For each random digit generated, each integer between 0 and 9 has a probability of .
10 being selected
o
If you generate 10 random digits, each integer between 0 and 9 much occur exactly
once
o
If you generated a very large number of random digits, then each integer between 0
and 9 would occur close to 10% of the time
o
The cumulative proportion of times that a 0 is generate tends to get closer to .10 as
the number of random digits generated gets larger and larger
5.2 How can we find probabilities?
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Sample space(S):
the set of all possible outcomes from a random phenomenon
o
Toss a fair coin: {H,T}
o
Roll a fair die:{1,2,3,4,5,6}
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Event:
a subset of the sample space possessing a designated feature, events are denoted
by capital letters
o
Aeven {2,4,6}
o
Bodd {1,3,5}
o
C5 {5}
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Tree diagram:
tool used to determine the outcomes of a sample space
o
Example in notebook
•
Probabilities for a sample space:
o
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 Spring '08
 smith
 Probability, Probability theory

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