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A machine 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?

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0.2647

0.2467

0.2746

0.2674

answer is A.

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Detailed Solution

$P (\bar{A}) = 0.14$

$P (A) = 1 - P (\bar{A}) = 1 - 0.14 = 0.86$

$P (B) = 1 - P (\bar{B}) = 1 - 0.1 = 0.9$

$P (C) = 1 - P (\bar{C}) = 1 - 0.05 = 0.95$

Given that A,B,C are independent events

$∴ P (M a c h i n e R u n n i n g) = P (A \cap B \cap C)$

$= P (A) P (B) P (C) = (0.86) (0.9) (0.95)$

$\begin{array}{l} = 0.7353 \\ ∴ P (M a c h i n e f a i l) = 1 - 0.7353 = 0.2647 \end{array}$

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