Asked Jun 25, 2019

An office has three smoke detectors. In case of fire, each detector has probability 0.9 of detecting it. If a fire occurs, what is the probability that at least one detector detects it?


Expert Answer

Step 1

Probability of at least one event occurring:

It is given that there are three smoke detectors and each detector has 0.9 probability of detecting fire.

The formula for the probability of at least one event occur is as follows.


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P(at least one event occur) 1- P(none of the events occur)

Step 2

Computation of probability that at least one detector detects fire:

The probability for each detector not detecting the fire is 1 – ...


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P(none of the three detector detects fire) 0.1x 0.1x 0.1 =0.001 P(at least one detector detects fire) 1-0.001 0.999


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