There is a 90% chance that a particular type of component will perform adequatel

Question

There is a 90% chance that a particular type of component will perform adequately under high temperature conditions. If the device involved has four such components, determine the probability of each of the following events by use of the formula for binomial probabilities.

a) All of the components perform adequately and therefore the device is operated.

b) The device is inoperative because exactly one of the four components fails.

c) The device is inoperative because one or more of the components fail.

Explanation / Answer

P(a component working) = 0.9

A) P(all components working)= 0.94 = 0.6561

B) P(1 component fails) = 4C1 x 0.93x0.1 = 0.2916

C) P(1 or more components fail) = 1-P(all componets work)

= 1-0.6561 = 0.3439

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