(a) A fire-detection device utilizes three temperature-sensitive cells acting in- dependently of each other in such a manner that any one or more may ac- tivate 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. (b) A geological study indicates that an exploratory oil well should strike oil with probability 0.2. What is the probability that the third strike comes on the seventh well drilled? What assumptions did you make to obtain this answer?

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