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A string of 10 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?

Option A:

0.06

Option B:

(0.06)^10

Option C:

1 – (0.06)^10

Option D:

(0.94)^10

Option E:

1 – (0.94)^10

Option E is the correct answer.

The string of light bulbs will fail if at least one light bulb fails. So, let’s find the probability of the opposite event and subtract that value from 1.

The opposite event is when none of the 10 light bulbs fails since the probability of each light bulb not to fail is 1-0.06=0.94 then the probability that none of the 10 light bulbs fails is 0.94^10.

Hence, the probability that at least one light bulb fails is 1-0.94^10.

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