A particular automatic sprinkler system for high-rise apartment buildings, offic

Question

A particular automatic sprinkler system for high-rise apartment buildings, office buildings, and hotels has two different types of activation devices for each sprinkler head. One type has a reliability of 0.91( that is, the probability that it will activate the sprinkler when it should be is 0.91). The other type, which operates independently of the first type, has a reliability of 0.87 Suppose a fire starts near a particular sprinkler head. What is the probability that the sprinkler head will be activated. 0.0117 0.9883 0.7917 None of the Above

Explanation / Answer

Since the probability that sprinkler will be activated for both types are independent of each other, therefore we will multiply these probabilities to get the probability that the sprinkler head will be activated. Hence,

the probability that the sprinkler head will be activated = 0.91x0.87 = 0.7917

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