Question

In: Statistics and Probability

Suppose that the failure rate (failing to detect smoke when smoke is present) for a brand...

Suppose that the failure rate (failing to detect smoke when smoke is present) for a brand of smoke detector is 1 in 2000. For safety, two of these smoke detector are

installed in a laboratory.

(a) What is the probability that smoke is not detected in the laboratory when smoke

is present in the laboratory?

(b) What is probability that both detectors sound an alarm when smoke is present in

the laboratory?

(c) What is the probability that one of the detectors sounds the alarm and the other

fails to sound the alarm when smoke is present in the laboratory?

Expert Solution

Solution: It is given:

The probability of failing to detect smoke when smoke is present is:

Let F be the events that denote the failure to detect.

The probability of detecting smoke when smoke is present is:

(a) What is the probability that smoke is not detected in the laboratory when smoke is present in the laboratory?

Answer: The probability that smoke is not detected in the laboratory when smoke is present in the laboratory is:

(b) What is probability that both detectors sound an alarm when smoke is present in the laboratory?

Answer: The probability that both detectors sound an alarm when smoke is present in the laboratory is:

(c) What is the probability that one of the detectors sounds the alarm and the other fails to sound the alarm when smoke is present in the laboratory?

Answer: The required probability is calculated as:

orchestra answered 1 year ago

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