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Chapter 4: Q4.11 (page 170)

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.

Short Answer

Expert verified

The answer isp=pk·(1-p)n-knkpk(1-p)n-k=1nk.

Step by step solution

01

Step 1:Given Information

We have that the probability the probability for ksuccesses in ntrials is simply nkpk(1-p)n-k.On the other hand ,the probability for some certain arrangement is pk·(1-p)n-k.

02

Step 2:Explanation

The probability for some certain arrangement given that we hadksuccesses inntrials is simplyp=pk·(1-p)n-knkpk(1-p)n-k=1nk.

03

Step 3:Final Answer

The answer isp=pk·(1-p)n-knkpk(1-p)n-k=1nk

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