A fire-detection device utilizes three temperature-sensitive cells acting independently of each other in such a manner that any one or more may activate the alarm. Each cell possesses a probability of p = 0.86 of activating the alarm when the temperature reaches 100° Celsius or more. LetY equal the number of cells activating the alarm when the temperature reaches 100°. (Round your answers to four decimal places.)(a) Find the probability distribution for Y.P(Y = 0) =P(Y = 1) =P(Y = 2) =P(Y = 3) =(b) Find the probability that the alarm will function when the temperature reaches 100°.

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Answered: (a) Find the probability distribution…

(a) Find the probability distribution for Y. P(Y = 0) = P(Y = 1) = P(Y = 2) = P(Y = 3) - (b) Find the probability that the alarm will function when the temperature reaches 100°.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 47E

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Question

A fire-detection device utilizes three temperature-sensitive cells acting independently of each other in such a manner that any one or more may activate the alarm. Each cell possesses a probability of p = 0.86 of activating the alarm when the temperature reaches 100° Celsius or more. Let
Y equal the number of cells activating the alarm when the temperature reaches 100°. (Round your answers to four decimal places.)
(a) Find the probability distribution for Y.
P(Y = 0) =
P(Y = 1) =
P(Y = 2) =
P(Y = 3) =
(b) Find the probability that the alarm will function when the temperature reaches 100°.

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