Question

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

Answer 1

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

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