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Chapter 8: Discrete Probability Distributions
For example
5! = 5
4
3
2
1 = 120
10! = 10
9
8
…
1 = 3,628,800
1! = 1
We define 0! = 1.
The Binomial Probability Distribution
The function that generates binomial probabilities is given below. It
represents the probability of exactly
successes in
trials in a binomial
experiment.
Note:
represents the number of combinations of
n
things taken
x
at a time
where the order of selection is not important. We sometimes denote this by
.
Example 8-11:
Ten items are selected at random from a production line.
What is the probability of selecting
exactly
2 defectives if it is known that
the probability of a defective item from this production system is 0.05?
Solution:
Let the number of defectives be represented by
X
. Then
X
is a
binomial random variable with
= 10,
= 2, and
= 0.05. Substituting into
the formula, gives
That is, the probability of observing 2 defectives in this binomial experiment
is 0.0746, correct to four decimal places.