Mathematics of Engineering  ME17
Spring 2008
Notes on Probability
Misunderstanding of probability may be the greatest of all impediments to scientiﬁc literacy
 Stephen Jay Gould
These notes cover material that you are responsible for, but which is not covered the
textbook.
Let
N
be the number of trials, and let
n
be the number of times a particular event
occurs in those
N
trials. The, the probability
p
of that particular event occurring is
deﬁned to be
p
= lim
N
→∞
n
N
.
(1)
Note that we must have 0
≤
p
≤
1.
Events are deﬁned to be
mutually exclusive
if only one of them can occur in a given
trial. The following rule applies to mutually exclusive events:
Rule 1
If
p
1
, p
2
,
···
p
r
are the separate probabilities of
r
mutually exclusive events, the
probability
P
that one of these events will occur in a given trial is
P
=
p
1
+
p
2
+
···
+
p
r
.
(2)
Events are said to be
independent
if the occurrence of any of them in no way inﬂuences
the probability of occurrence of any other. The following rule applies to independent
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 Fall '09
 Probability, Probability theory, mutually exclusive events, welldeﬁned deﬁnition

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