A string of 13 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 0.02, what is the probability that the string of light bulbs will fail during the time period T?
Choose the correct choice from the following answers:	A) 0.02	B) (0.02)^13	C) 1 - (0.02)^13	D) (0.98)^13	E) 1 - (0.98)^13
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 13 light bulbs fails, since the probability of each light bulb not to fail is 1-0.02= 
<gadget id="calculator">1-0.02</gadget>
<output>0.98</output>
0.98 the the probability that none of the 13 light bulbs fails is 0.98^13.   Hence, the probability that at least one light bulb fails is 1-0.98^13.   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 13, then according to your logic the probability that the string of light bulbs will fail would be 100*0.02= 
<gadget id="calculator">100*0.02</gadget>
<output>2</output>
2, which is not possible since the probability of an event cannot be more than 1 (100%).
<result>E</result>
A string of 13 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 0.02, what is the probability that the string of light bulbs will fail during the time period T?