Problem 1 There are three power plants in a small utility system, call them X, Y

Question

Problem 1 There are three power plants in a small utility system, call them X, Y, and Z. The sample space for the three power plants can be written in parenthesis shorthand where a 0 means a specific plant is not operating and a 1 means a specific plant is operating. The power plant status is shown in order of X, Y, and Z in the parenthesis. So for example, (0, 1,1) means that power plant X is not operating and that Y and Z are operating. The sample space is shown in the following figure with the probabilities associated with each event (0,0,0) , 0. 0) 0.07 0.16 004 0.18 0.03 0.21 0.18 0.13 What is: I) The probability that only one power plant is not operating? 2) The probability that one or more power plants is not operating? 3) The probability that plant X is not operating? 4) The probability that plant Z is operating and one other plant is not operating?

Explanation / Answer

1) The probability that only one power plant is not operating is 0.16 + 0.04 + 0.03 = 0.23

2. The probability that one or more power plants is not operating is
P(X=1) + P(X=2) + P(X=3) = 0.23 + (0.18+0.21+0.18) + 0.13 = 0.93

3. P(Plant X is not operting) = 0.07+0.04 +0.03+0.18 = 0.32

4. P(Plant Z is operating and one other plant is not operating) = 0.18+ 0.18 = 0.36

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