Difficult Math Problem #84 - Probability

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800guy
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Topic: Difficult Math Problem #84 - Probability
PostMon Jan 08, 2007 3:49 pm
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A serial set consists of N bulbs. The serial set lights up only if all the N bulbs are in working condition. Even if one of the bulbs fails then the entire set fails. The probability of a bulb failing is x. What is the probability of the serial set failing?

OA coming after a few people try to answer. Source: Difficult Math Problems doc on this forum
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PostTue Jan 09, 2007 1:00 am
prob. of working (1-x) so prob of N working is (1-x)^N and set will not work when at least one fails and --> p=1-(1-x)^N
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800guy
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PostWed Jan 10, 2007 9:05 am
OA:

Probability of x to fail. Probability of a bulb not failing = 1-x
probability that none of the N bulbs fail, hence serial set not failing = (1-x)^N
probability of serial set failing = 1-(1-x)^N
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