In Chapter 4 we will continue our discussion of discrete random variables and wi

Question

In Chapter 4 we will continue our discussion of discrete random variables and will return to continuous variables in Chapter 5. Exercises 1. Two parts of a machine are manufactured independently. These two parts have probabilities P1 and p2 respectively of failing. Find the probability that (a) neither part fails (b) at least one part fails (c) exactly one part fails. 2. A component A which has 90 per cent reliability (it will fail one in ten times) is vital to the running of a machine. An identical component is fitted in parallel to form system S, and the machine will work provided that one of these components functions correctly Find the reliability of system S 53 Exercises

Explanation / Answer

Ans:

1)

a)P(nether part fails)=(1-p1)*(1-p2)

b)P(at least one part fails)=1-P(none of them fails)=1-(1-p1)(1-p2)

c)P(exactly one fails)=(1-p1)p2+p1*(1-p2)

2)

Reliability of component A=0.9

Probability of failure for component A,p=1-0.9=0.1

System will survive if atleast one of the component is working,so

Reliability of the system=P(atleast one of the components works)=1-P(none of them works)

=1-0.1*0.1

=1-0.01

=0.99

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