Question

The operates if all of its three components function. The probability that the first component fails during the year is 0.14, the second component fails is 0.10 and the third component fails is 0.05. What is the probability that the machine will fail during the year? Select the correct answer from above options

Answer 1

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))]`.