A string of 30 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 0.1, what is the probability that the string of light bulbs will fail during the time period T? Choose the most appropriate option.
A) 0.1 B) ( 0.1 ) ^ 30 C) 1 - ( 0.1 ) ^ 30 D) ( 0.93 ) ^ 30 E) 1 - ( 0.90 ) ^ 30

Rationale: "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 30 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.1 = 0.90 the the probability that none of the 30 light bulbs fails is 0.90 ^ 30 . hence , the probability that at least one light bulb fails is 1 - 0.90 ^ 30 . answer : e . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 30 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.1 = 10 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) ."
Answer: E