Question

A computer has three mutually independent components: a CPU, a MONITOR, and a KEYBOARD. The probability...

A computer has three mutually independent components: a CPU, a MONITOR, and a KEYBOARD. The probability of failure within six years for these components is given as 0.50, 0.20, and 0.10 respectively. What is the probability that the computer is fully functioning.
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Answer #1

Probability that CPU have not failed in 6 years = 1 - 0.5 = 0.5

Probability that MONITOR have not failed in 6 years = 1 - 0.2 = 0.8

Probability that KEYBOARD have not failed in 6 years = 1 - 0.1 = 0.9

Probability that the computer is fully functioning = probability of failure that none of the components failed

= Probability that CPU have not failed in 6 years * Probability that MONITOR have not failed in 6 years * Probability that KEYBOARD have not failed in 6 years

= 0.5 * 0.8 * 0.9

= 0.36

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