Chapter 4 – Introduction to Probability

Probability
is a numerical measure of the likelihood that an event will occur. Probability
values are always assigned on a scale from 0 to 1; a probability near zero indicates an
event is unlikely to occur, and a probably near 1 indicates an event is almost certain to
occur
Experiments, Counting Rules, and Assigning Probabilities

An
experiment
is a process that generates welldefined outcomes. During the repetition
of an experiment, one and only one of the possible experimental outcomes will occur

The
sample space
for an experiment is the set of all experimental outcomes

An experimental outcome is also referred to as a
sample point
to identify it as an element
of the sample space
Counting Rules, Combinations, and Permutation

The counting rule for multiplestep experiments can be expressed as:
If an experiment can be described as a sequence of
k
steps with
n
1
possible outcomes on
the first step,
n
2
on the second and so on, then the total number of experimental outcomes
is given by
(n
1
)(n
2
)…(n
k
)

A
tree diagram
is a graphical representation that helps visualize a multiplestep
experiment (Figure 4.2)

A second counting rule allows one to count the number of experimental outcomes when
the experiment involves selecting n objects from a set of N objects
(Equation 4.1 p. 145)

The notation
!
means factorial; for example, 5 factorial is 5! = (5)(4)(3)(2)(1) = 120

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 Fall '07
 Thornton
 Conditional Probability, experimental outcomes

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