Math 120 SP08 SBrodnick
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1
7.2
: Estimated & Theoretical
Probability
2
7.2: Estimated & Theoretical Probability
*
Estimated Probability
is based on actual
data
*
Theoretical Probability
is based on
intuition
*Est. Prob. of event E:
P(E) =
*Theoretical Prob. of event E:
P(E) =
frq(E)
N
# of times event E occurs (frequency of E)
# of times experiment is performed
(# of trials / sample size)
# of favorable outcomes
total # of possible outcomes
=
n(E)
n(S)
3
*
Collection of all of the outcomes and their
probabilities:
*
Properties
:
1.
Prob. of each outcome is a
number between 0 and 1 (including 0 & 1)
2.
Prob.’s of all events add up to 1
3.
Prob. of an event E is the sum of the
prob.’s of individual outcomes in E
7.2: Estimated & Theoretical Probability
Probability Distribution
4
Examples
:
1. Toss a coin 100 times
Event E: Heads
You toss heads 43 times
P
(
E
) = ?
2.A die is rolled 50 times.
The frequency of
each roll is listed below.
Find the
est. prob.
distribution
.
Roll:
1
2
3
4
5
6
Freq:
9
11
6
10
6
8
7.2: Estimated & Theoretical Probability
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3.
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 Spring '08
 Brodnick
 Math, Probability, Probability theory, #, AUB

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