The space shuttle flight control system uses three independent computers working

Question

The space shuttle flight control system uses three independent computers working in parallel. At each critical step, the computers vote to determine the appropriate step. The probability that a computer makes a wrong decision is 0.0001. Let X denote the number of computers that make a wrong decision in a critical step. a) What kind of distribution does X follow and what are the associated parameters? b) What is the probability of all computers making a wrong decision in a critical step? c) What is the probability that all computers make the right decision in a critical step? d) What is the probability that at least one computer makes the wrong decision in a critical step? e) Let's now assume that the probability that the first computer makes a wrong decision in a critical step is 0.0009, the second one, 0.0008 and the third one 0.0007. What is the probability of all computers making wrong decisions in a critical step?

Explanation / Answer

A-X follows Binomial distribution with n=3 and p=0.0001. Here p is the probability of a wrong decision by computer

B-P(X=3)=0 approximately using excel function =BINOMDIST(3,3,0.0001,FALSE)

C-All the computers make the right decision means no computer make wrong decision,

So we have to find P(X=0)=0.9997 using excel function =BINOMDIST(0,3,0.0001,FALSE)

D-P(X>=1)=1-P(X=0)=1-0.9997=0.0003

E-P(all wrong decisions)=0.0009*0.0008*0.0007=0.000000000504

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