Question

a machine operates, if all 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 is 0.05. what is the probability that the machine will fail during the year?

Answer 1

The probability that the machine will fail during the year is approximately 0.2683, or 26.83%.

Step-by-step explanation:

To find the probability that the machine will fail during the year, we can find the complement of the probability that all three components function.

Probability that the first component fails = 0.14
Probability that the second component fails = 0.10
Probability that the third component fails = 0.05

The probability that all three components function = (1 - 0.14) * (1 - 0.10) * (1 - 0.05) = 0.86 * 0.9 * 0.95 = 0.7317.

Therefore, the probability that the machine will fail during the year is approximately 1 - 0.7317 = 0.2683, or 26.83%.