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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.3 - Problem 37e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.3 - Problem 37e

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# A system contains two components, C and D, connected in ISBN: 9780073401331 38

## Solution for problem 37E Chapter 2.3

Statistics for Engineers and Scientists | 4th Edition

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Problem 37E

A system contains two components, C and D, connected in parallel as shown in the diagram. Assume C and D function independently. For the system

to function, either C or D must function.

a. If the probability that C fails is 0.08 and the probability that D fails is 0.12, find the probability that the system functions.

b. If both C and D have probability of failing, what must the value of be so that the probability that the system functions is 0.99?

c. If three components are connected in parallel, function independently, and each has probability of failing, what must the value of be so that the probability that the system functions is 0.99?

d. If components function independently, and each component has probability 0.5 of failing, what is the minimum number of components that must be connected in parallel so that the probability that the system functions is at least 0.99?

Step-by-Step Solution:

Step 1 of 4

a) Here C and D are 2 conductors connected parallely  and function independently

P(C fails)=P(C’)

=0.08

P(C function)=P(C)

=1-0.08

=0.92

P(D fails)=P(D’)

=0.12

P(D function)=P(D)

=1-0.12

=0.88

P(That the system function)=P(CUD)

=P(C)+P(D)-P(C)P(D)

=0.92+0.88-0.92(0.88)

=0.9904

Step 2 of 4

Step 3 of 4

##### ISBN: 9780073401331

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