Stats: Other Discrete Distributions
Multinomial Probabilities
A multinomial experiment is an extended binomial probability. The difference is that in a multinomial
experiment, there are more than two possible outcomes. However, there are still a fixed number of
independent trials, and the probability of each outcome must remain constant from trial to trial.
Instead of using a combination, as in the case of the binomial probability, the number of ways the outcomes
can occur is done using distinguishable permutations.
An example here will be much more useful than a formula.
The probability that a person will pass a College Algebra class is 0.55, the probability that a person will
withdraw before the class is completed is 0.40, and the probability that a person will fail the class is 0.05.
Find the probability that in a class of 30 students, exactly 16 pass, 12 withdraw, and 2 fail.
Outcome
x
p(outcome)
Pass
16
0.55
Withdraw
12
0.40
Fail
2
0.05
Total
30
1.00
The probability is found using this formula:
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 Spring '07
 Bagwhandee
 Binomial, Probability, Probability theory, Binomial distribution, Binomial probability, Simeon Poisson, Hypergeometric Probabilities

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