Question: A fire-detection device uses three temperature-sensitive cells acting independently of one another in such a manner that any one or more can activate the alarm.

A fire-detection device uses three temperature-sensitive cells acting independently of one another in such a manner that any one or more can activate the alarm. Each cell has a probability p = .8 of activating the alarm when the temperature reaches 135°F or higher. Let x equal the number of cells activating the alarm when the temperature reaches 135°F.
a. Find the probability of x.
b. Find the probability that the alarm will function when the temperature reaches 135°F.
c. Find the expected value and the variance for the random variable x.

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