What is the probability that a string of ten goes out during that period of time?
Matthew Martinez 
Some string of holiday lights are wired in series; thus, if one bulb fails the entire string goes out.
Suppose the probability of an individual bulb failing during a certain period of time is 0.05.
What is the probability that a string of ten goes out during that period of time?
State the assumptions you make concerning the light bulbs.
(Answer: 0.4013)
I'm just not sure how to approach the question. I think it has something to do with Bayes theorem but I'm not sure how to apply it in this case.
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$\begingroup$$P(\text{That a string of ten goes out}) = 1- P(\text{That a string of ten doesn't go out})$
We know that $P(\text{That a string of ten doesn't go out}) = (0.95)^{10}$
Our desired probability is $1- (0.95)^{10} = 0.4013$
$\endgroup$ $\begingroup$If at the end all bulbs are on, that means no one has failed, 10 bulbs 0.95 probability of not failure results in $0.95^{10} = 0.5987$. So the opposite situation is $1-0.5987=0.4013$.
The trick is simple, an AND condition means multiply, in this case multiply 0.95 ten times by itself.
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