6. Suppose two components are connected in a series, so that the whole system wo

Question

6. Suppose two components are connected in a series, so that the whole system works if and only if both components work. Each component consists of two units connected in parallel, so that the t works as long as either unit works. Thus we have 2 components attached to each other (both must work), with each component com- prising of 2 units (at least 1 unit must work for single component to work). Assume all units are independent and fail with probability p (work with probability 1 -p). Also assume the components are independent of each other. What is the probability the whole system works? Hint: The probability a single component wil work is equal to one minus the probability of the component not working (which occurs when both units within component dont work

Explanation / Answer

P(a component working) = P(any one of the two units working)

= 1 - P(both units not working)

= 1 - p2

So, the probability that the whole system works = P(both components working) = (1 - p2)2

1 - 2p2 + p4

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