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I am working the following probability problem which I came across online:

A computer network has 5 paths to its destination. Each path has a 20% chance of working and each path is independent. Am I guaranteed that at least one path will work?

I first answered it like:

P(1st path working OR 2nd path working OR 3rd path working OR 4th path working OR 5th path working) = 0.2 + 0.2 + 0.2 + 0.2 + 0.2 = 1

but apparently that is not correct. Can someone explain why?

Thanks!

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    So if the probability that each path works were $30\%$ instead of $20\%$, would you have said that the probability of at least one path working is $0.3+0.3+0.3+0.3+0.3=1.5$?2012-04-21

2 Answers 2