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What is the probability that no 2 neighboring components are both non-functional?
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 non-functional?
Topic: Random Variables
From: A First Course in Probability by Sheldon Ross
Let's look at small value of n and see if we notice a pattern...
n=2 Arrangement: AB
The probability of them both being functional would be p^2
n=3 Arrangement: ABC
There are two pairs: AB and BC. The probability that both A and B are non-functional and C is functional is (1-p)^2p. The probability that both B and C are non-functional and A is functional is p(1-p)^2. The probability that all three are non functional is (1-p)^3. Final probability: 1 - 2p(1-p)^2 - (1-p)^3
n=4 Arrangement: ABCD.
Arrangements of non-functioning units to subtract out: AB, BC, CD, ABC, BCD, ABCD
Final probability: 1 - 3(1-p)^2p^2 - 2(1-p)^3p - 1(1-p)^4
n=5 Arrangement: ABCDE
Arrangements of non-functioning units to subtract out: AB, BC, CD, DE, ABC, BCD, CDE, ABCD, BCDE, ABCDE
Final probability: 1 - 4(1-p)^2p^3 - 3(1-p)^3p^2 - 2(1-p)^4p - 1(1-p)^5
The pattern seems to be:
1 - (n-1)(1-p)^2p^(n-2) - (n-2)(1-p)^3p^(n-3) - (n-3)(1-p)^4p^(n-4) - ... - (1-p)^n
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Mid-America 18" x 55" Bright White P3 Raised Panel Vinyl Exterior Shutters (Pair)
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DescriptionBrand: Mid-America. Custom-made. Shutter mounting hardware included. Made of lightweight fade-resistant vinyl. Easy installation on any surface. Natural-looking straight top. See site for additional custom options... Features
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HTY All Natural Taiwanese Functional Candies - Black Seasame with Senna Seed Chewy Candy For Constipation Relief - 5.6 Oz
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Runtime Error Pure Virtual Function Call - Repair it in Seconds!
It is often aggravating and nerve-wracking, and perhaps lead you to feel helpless while getting a runtime error pure virtual function call on your monitor. Lots of people can't begin to understand why these problems occur and how they can be solved. Before deciding to hire a computer technician at great expense, study this brief how-to guide since it will teach you a simple method to get rid of these problems almost instantly.
Before we begin, allow me to explain a bit about how your windows is organized so that you'll learn why these error messages are a problem with your pc. Many of these runtime errors are the result of a 'contaminated' or damaged registry system - this is the place where windows tracks what happens on your pc, thus any time you install, uninstall, or update any piece of software or hardware, your windows program keeps track of it.
The registration function covers many kinds of data; sections of it contain the links that communicate to windows where the files that manage your assorted software/hardware applications are situated. It can sometimes happen that an incorrect software installation or removal might cause non-functioning links in your registry system, in simple words, windows can't operate that software or part of it, which might lead to your getting a runtime error pure virtual function call and many other problems such as blue screens, freeze ups, slow performance and more. These sorts of problems are easy to solve if you are a specialist and you are comfortable "playing" with your windows registry, for most people, however, it's not advisable to go it alone - you can make a bad situation even worse!
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