A fire-detection device utilizes three temperature-sensitive cells acting indepe

Question

A fire-detection device utilizes three temperature-sensitive cells acting independently of each other in such a manner that anyone or more may activate the alarm. Each cell possesses a probability p = 0.8 of activating the alarm when the temperature reaches 100 degrees Celsius. Let Y equal the number of cells activating the alarm when the temperature reaches 100 degrees. Find the probability distribution of Y. Find the probability that the alarm will function when the temperature reaches 100 degrees.

Explanation / Answer

here as n=3 and p=0.8 ; it is binomial distribution. cause trails are fixed and probabilty is independent.

hence probabilty disribution of Y is as follows:

P(Y)=3Cy (0.8)y(0.2)3-y

probabilty that alarm function =1-P(all three cell will not work) =1-(0.2)3 =0.992

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