The operates if all of its three components function. The probability that thefirst component fails during the year is 0.14, the second component fails is0.10 and the third component fails is 0.05. What is the probability that themachine will fail during the year?

The operates if all of its three components function. The probability

1.	The operates if all of its three components function. The probability that thefirst component fails during the year is 0.14, the second component fails is0.10 and the third component fails is 0.05. What is the probability that themachine will fail during the year?
Answer» Correct Answer - 0.2647 Let `E_(1), E_(2), E_(3)` be the respective events that the 1st, 2nd and 3rd components function. Then, `P(bar(E)_(1))=0.14, P(bar(E)_(2))=0.10` and `P(bar(E)_(3))=0.05` `implies P(E_(1))=(1-0.14)=0.86, P(E_(2))=(1-0.10)=0.90` and `P(E_(3))=(1-0.05)=0.95` `implies` P(machine fails) `=1 -P` (machine functions) `=1-P [(E_(1) and E_(2) and E_(3))]` `=1-[P(E_(1))xxP(E_(2))xxP(E_(3))]`.

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The operates if all of its three components function. The probability that thefirst component fails during the year is 0.14, the second component fails is0.10 and the third component fails is 0.05. What is the probability that themachine will fail during the year?

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