A man has two lights in his well house to keep the pipes fro

A man has two lights in his well house to keep the pipes from freezing in winter. He checks the lights daily. Each light has probability 0.002 of burning out before it is checked the next day (independently of the other light).

A.If the lights are wired in parallel one will continue to shine even if the other burns out. In this situation, compute the probability that at least one light will continue to shine for the full 24 hours. Note the greatly increased reliability of the system of two bulbs over that of a single bulb.

B.If the lights are wired in series neither one will continue to shine even if only one of them burns out. In this situation, compute the probability that at least one light will continue to shine for the full 24 hours. Note the slightly decreased reliability of the system of two bulbs over that of a single bulb.

Solution

A)

P(at least one will light) = 1 - P(no one will light)

= 1 - (0.002)^2

= 0.999996 [answer]

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b)

Here, both bulbs must light, because both will not light if the other burns out.

Thus,

P(at least one will light) = P(both will light)

= (1-0.002)^2

= 0.996004 [ANSWER]