4. Three components are assembled together to form a pot (such as a pot with a l

Question

4. Three components are assembled together to form a pot (such as a pot with a lid, a body, and a handle).
The first component will be scratched after assembly with probability 0.005
The second component will be scratched after assembly with probability 0.004.
The third component will be scratched after assembly with probability 0.003.

Assume that whether or not a component is scratched is independent of whether or not any other component or pair of components is scratched. Here is a set of elementary outcomes for the next product to be assembled:
{SSS, SSN, SNS, NSS, NNS, NSN, SNN, NNN}
In the above set, entry NSN means the first component is not scratched, the second component is scratched, and the third component is not scratched. The other entries have similar meanings.
Define A to be the event that the first component is scratched. Define B to be the event that the second component is scratched. Define C to be the event that the third component is scratched.

A) List all the elementary outcomes for which A will happen, all the elementary outcomes for which B will happen, and all the elementary outcomes for which C will happen.
B) List all the elementary outcomes for which A or B or C will happen
C) explain what a reasonable value for P(A) is 0.005
D) Explain why P(A U B U C) does not equal P(A) + P(B) + P(C ).

Explanation / Answer

Let A to be the event that the first component is scratched. Define B to be the event that the second component is scratched. Define C to be the event that the third component is scratched ---------------------------------------------------------------------------------------- A)List all the elementary outcomes for which A will happen =SSS, SSN, SNS,SNN List of all elementary outcomes for which B will happen =SSS,SSN,NSS,NSN LIst of all the elementary outcomes for which C will happen =SSS,SNS,NSS,NNS ----------------------------------------------------------------------------------------- B)List of all the elementary outcomes for which A or B or C will happen =SSS,SSN,SNS,NSS,SNN,NNS,NSN ---------------------------------------------------------------------------------------- c) Theres are 4 possible outcomes of A out of 8 So P(A)=4/8=.5 So 0.005 is not a reaonalbe value for P(A) ------------------------------------------------------------------------------------------ D) Since there are common events for A , B and C, P(AUBUC) is not equal to P(A)+P(B)+P(C) -------------------------------------------------------------------------------------------

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