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6.1 Assigning Probabilities to Events
•
Random experiment
– process or course of action that results in one of
a number of possible outcomes.
The outcome cannot be predicted.
ie – the flip of a coin, roll of a die
•
To determine the probability that a particular outcome will occur, we
first need to know all
possible outcomes.
List them!
•
Sample space
– a list of all possible outcomes, usually denoted with an
S = {O
1
, O
2
, … , O
n
}
•
Simple events
– individual outcomes O
1
, O
2
,…
•
Event
– a collection of one or more simple events
For example
:
If our experiment is rolling a die:
the sample space S = {1,2,3,4,5,6}
If Event A is defined to be an even number then A = {2,4,6}
•
Ultimately we want to find the probability that an event happens, P(A).
•
The probability of Event A is equal to the sum of the probabilities
assigned to the simple events contained in A.
P(A) = P(2) + P(4) + P(6)
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View Full Document Requirements of Probabilities
If E
i
represents the simple events, so S = {O
1
, O
2
,…, O
n
}
then:
∑
=
=
≤
≤
n
i
i
i
O
P
i
O
P
1
1
)
(
)
2
each
for
1
)
(
0
)
1
The probability of any outcome must
lie between 0 and 1, inclusive.
The sum of the probabilities of all the
outcomes in a sample space must be
1.
Example
Flip a coin twice
S = {HH, HT, TH, TT}
Four simple events, each event equally likely, so each simple event
has a probability of ¼.
Warning!!!!
You won’t always have experiments where each simple
event is equally likely.
Each of the events in this problem is equally
likely because, with a fair coin, H and T are equally likely.
When
that is not the case, you will be given or will have to calculate the
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This note was uploaded on 04/09/2008 for the course MTHSC 309 taught by Professor Cathydavis during the Spring '08 term at Clemson.
 Spring '08
 CathyDavis
 Statistics, Probability

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