binomial(n, p) The probability distribution for a binomial random variable X ~ where n is the number of trials and p the success probability, is: n! P(X = x) = k!(n – k)!P*(1 – p)"-k Explain the role of n! k! (n-k)! in the equation above.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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A lecturer is interested in studying the pass rate of their module. In a particular year, 20 students sit the module and 3 students fail.

 

 

binomial(n, p)
The probability distribution for a binomial random variable X ~
where n is the number of trials and p the success probability, is:
n!
P(X = x) =
k!(n – k)!P^(1 – p)"-k
n!
Explain the role of
k!(n-k)! in the equation above.
Transcribed Image Text:binomial(n, p) The probability distribution for a binomial random variable X ~ where n is the number of trials and p the success probability, is: n! P(X = x) = k!(n – k)!P^(1 – p)"-k n! Explain the role of k!(n-k)! in the equation above.
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