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Stat 250 Gunderson Lecture Notes
Chapter 7: Probability
Chance favors prepared minds.
 Louis Pasteur
Many decisions that we make involve uncertainty and the evaluation of probabilities.
Example:
Roll a fair die
possible outcomes = {
1, 2, 3, 4, 5, 6
}
Before you roll the die do you know which one will occur?
No
What is the probability that the outcome will be a ‘4’?
1/6 = P(‘4’)
Why?
A few ways to think about PROBABILITY:
(1) Personal or Subjective Probability
P(A) = the degree to which a given individual believes that the event A will happen.
(2) Long term relative frequency
P(A) = proportion of times ‘A’ occurs if the random experiment (circumstance) is repeated
many, many times.
(3) Basket Model
P(A) = proportion of balls
in the basket that have
an ‘A’ on them.
Note: each time I do the experiment,
the selected ball is either white or blue;
once I look, there is no more ‘probability’)
Note:
A probability statement
IS NOT
a statement about
INDIVIDUALS
.
It
IS
a statement about
the population / the basket of balls
.
7.3 Probability Definitions and Relationships
7.4 Basic Rules for Finding Probability
There is a lot you can learn about probability. One basic rule to always keep in mind is that the
probability of any outcome is always between 0 and 1.
Now, there are entire courses devoted just to
studying probability.
But this is a Statistics class.
So rather than start with a list of definitions and
formulas for finding probabilities, let’s just do it through an example so you can see what ideas about
probability we need to know for doing statistics.
10 balls: 3 blue and 7 white; One ball will be selected at random.
What is P(blue)? __
3/10
__
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Example:
Shopping Online
Many Internet users shop online.
Consider a population of 1000 customers that shopped online at a
particular website during the past holiday season and their results regarding whether or not they
were satisfied with the experience and whether or not they received the products on time.
These
results are summarized below in table form.
Using the idea of probability as a proportion, try
answering the following questions.
On Time
Not On Time
Total
Satisfied
800
20
820
Not Satisfied
80
100
180
Total
880
120
1000
May decide to not include the probability notation P(…) the first time through.
a.
What is the probability that a randomly selected customer was satisfied with the experience?
Think about probability as proportion, so 820/1000 = 0.82
or 82%
This would be represented by P(Satisified).
b.
What is the probability that a randomly selected customer was
not
satisfied with the experience?
Well if 82% were satisfied, then 1 – 0.82 = 0.18 or 18% were
not
satisfied. Would be
represented by P(Not Satisfied), and you just used what we call the complement rule.
c.
What is the probability that a randomly selected customer was both satisfied
and
received the
product on time?
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 Winter '10
 Gunderson
 Statistics, Probability, Diabetes

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