suppose a certain brand of smoke detector functions properly 85 percent of the time. i installed 3 of thse in my room, what is probability that at least one of the three smoke detectors functions propoerly

The probability that at least one of the three smoke detectors functions properly = 0.996625

Step-by-step explanation:

Given that:

a certain brand of smoke detector functions properly 85 percent of the time

Let X represent the certain brand of smoke detector

X = 85%

X = 0.85

Let the probability that at least one of the three smoke detectors functions properly be P(Y)

P(Y) = 1-  (1 - X)³

P(Y) =1 -  (1 - 0.85)³

P(Y) = 1 -  0.003375

P(Y) = 0.996625

∴

The probability that at least one of the three smoke detectors functions properly = 0.996625

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step-by-step explanation: