Gomez Office Supply has installed three smoke detectors in its stockroom.The installer asserts that each detector is 90% likely to detect a fire within 30 seconds of ignition.Assuming the three detectors function independently, how likely is it that a fire will be detected within 30 seconds?
A).100
B).001
C).300
D).999
E).270

Question

Quizplus · Accepted Answer

The probability that a fire will not be detected by a single detector is 1 - 0.90 = 0.10. Since the detectors function independently, the probability that none of the three detectors will detect the fire is 0.10 * 0.10 * 0.10 = 0.001. Therefore, the probability that at least one detector will detect the fire is 1 - 0.001 = 0.999 or 99.9%.

Gomez Office Supply Has Installed Three Smoke Detectors in Its