Question

In: Statistics and Probability

A smoke – detector system uses two devices, A and B, which operate independently. When the...

A smoke – detector system uses two devices, A and B, which operate independently. When the smoke is present, the probability that it will be detected by device A is 0.96, the probability that it will be detected by device B is 0.92. a. When the smoke is present, probability that it will be detected by both devices is ________ b. When the smoke is present, probability that it will be detected by at least one device is ________ c. When the smoke is present, probability that it will not be detected by either device is________

Expert Solution

Answer:

Given that

P(A) = 0.96

P(B) = 0.92

(a) We have to find the probability that smoke is detected by both devices:

P(smoke is detected by both devices) = P ( A ∩ B )

= P ( A ) × P ( B ) .

= 0.96 × 0.92

P(smoke is detected by both devices) = 0.8832

Therefore the required probability is 0.8832

(b) We have to find the probability that smoke will be detected by at least one device:

P(smoke will be detected by at least one device) = P(A∪B)

P(smoke will be detected by at least one device) = P(A)+P(B) −P(A∩B)

= 0.96 + 0.92 - 0.8832

= 1.88 - 0.8832

P(smoke will be detected by at least one device) = 0.9968

Therefore the required probability is 0.9968

(b) We have to find the probability that smoke will not be detected by either device:

P(smoke will not be detected by either device) = 1- P(A∪B)

P(smoke will not be detected by either device) = 1 - 0.9968

P(smoke will not be detected by either device) = 0.0032

Therefore the required probability is 0.0032

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orchestra answered 1 year ago

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