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Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink]
Exhausting all the options and combinations (from 1 bulb failing to all bulb failing) would likely take you 10+ minutes - not a wise idea when you have 35 minutes for 20 questions.
We can decompose the probabilities like this:
We are told that if even just one bulb fails, the entire string fails.
Therefore:
P(at least one fails)+P(no failures)=1
P(at least one fails)=1-P(no failures)
P(no failure) is just the probability that all the bulbs dont fail which is given to us in the stem:
P(fail)=0.06, implying that P(no fail)=0.94
So p(no failure)=0.94^10,
and P(at least one fails)=1-(0.94^10)
which is exactly option E
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