Introducing Probability:
Chapter 5
Section 5.1
Probability Rules:
A
Introduction: Probability
=Mathematics of Chance.
Probability is a measure of the likelihood of a given event.
B
(a)
Formal Definition:
Probability= p =
f/N
=
Number of successes / number of trials
(b)
f= number of successes in
NTrials of a random experiment.
N= Number of Trials.
p = probability of success, when an experiment is repeated many times.
C
Example
What proportion of adults played the lottery last year?
In a sample of 1523
adults we found that 868 answered yes to this question
Hence
p = 868/1523 = 57=57%
adults we found that 868 answered yes to this question.
Hence,
p = 868/1523 = .57=57%.
If we chose another sample, we might get the sample proportion of, say "p = .54" or "p=.60" which is different due to chance.
If sample proportion is "p=.37'", we should question our sampling
procedure because "p=.37 is too far from what we expected.
D
Law of Large Numbers
: As
N increases, sample proportion approaches "TRUE" Probability.
E Idea of Probability:
(Chance behavior unpredictable in the short run, but over time quite predictable.)
Example
Toss a coin 5000 times. Trial A: Pattern=THTT….
Trial B: HHHHH….
Note: The pattern
is quite different over the short run; but after 5000 tosses you expect something
CLOSE
to 2500 heads and 2500.
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 Spring '08
 Unkown
 Math, Statistics, Probability, Probability theory

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