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A First Course in Probability
Found in: Page 170
A First Course in Probability

A First Course in Probability

Book edition 9th
Author(s) Sheldon M. Ross
Pages 432 pages
ISBN 9780321794772

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Short Answer

There are n components lined up in a linear arrangement. Suppose that each component independently functions with probability p. What is the probability that no 2 neighboring components are both nonfunctional?

The answer isPElocalid="1646910197664" =0m(n+1)/2n+m-1mpn-m(1-p)m

See the step by step solution

Step by Step Solution

Step 1:Given Information

Let X denotes the number of non functional components and let E denotes the event. if no two nonfunctional components are to be constructive, then the space between the functional components must each contain at most one non functional components.

Step 2:Calculation

PE=m=0nP(EX=m)P(X=m),(From Bayes theorem)


localid="1646910154485" =0m(n+1)/2n+m-1mnmnmpn-m(1-p)m

localid="1646910170371" =0m(n+1)/2n+m-1mpn-m(1-p)m

Step 3:Final Answer

The answer is PElocalid="1646910184882" =0m(n+1)/2n+m-1mpn-m(1-p)m

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