A power plant supplies electric power for five cities 1-5 via high voltage power lines A-E, as shown in attachment. Suppose that a 7.0 earthquake will damage each high voltage power line independently...

A power plant supplies electric power for five cities 1-5 via high voltage power lines A-E, as shown in attachment.

Suppose that a 7.0 earthquake will damage each high voltage power line
independently with probability 0.2. A city has electric power only if all the high voltage power lines between the city and the power plant are intact.

Let X denote the number of cities that lose electric power when a 7.0 earthquake hits. For instance, if power line C is the only one damaged, then X = 1 (city 3 loses power); if power line B is the only one damaged, then X = 2 (both cities 2 and 3 lose power).

(a) Find P{X = 0} and P{X = 5}.
(b) When a 7.0 earthquake hits, what is the probability that city 3 loses electric power, and what is the probability that city 5 loses electric power?
(c) Compute E[X].

Extracted text: Power 2 B - 1 A E 5 Plant 3 4