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Consider n independent sequential trials, each of which is

Chapter 4, Problem 11TE

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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.

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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.

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