Solution Found!
Consider n independent sequential trials, each of which is
Chapter 4, Problem 11TE(choose chapter or problem)
Consider n independent sequential trials, each of which is successful with probability p. If there is a total of k successes, show that each of the \(n ! /[k !(n-k) !]\) possible arrangements of the k successes and n - k failures is equally likely.
Questions & Answers
QUESTION:
Consider n independent sequential trials, each of which is successful with probability p. If there is a total of k successes, show that each of the \(n ! /[k !(n-k) !]\) possible arrangements of the k successes and n - k failures is equally likely.
ANSWER:Step 1 of 2
From the given information we consider ‘n’ independent sequential trials, each of which is successful with probability p.
Our goal is:
We need to show that each of the \(\frac{n !}{k !(n-k) !}\) possible arrangements of the k successes and \((n-k)\) failures are equally likely.