Question

A wind farm operator is trying to assess the cost associated with each turbine. On a stormy
day, a turbine breaks down with probability 0.2. On a non-stormy day, the probability that
a turbine breaks down is equal to 0.1. Weather analysis reveals that the probability of a day
being stormy is 0.4, independently of other days. When wind turbines are co-located, they
break down in a conditionally independent manner given the weather.
(a) If a day is selected at random, what is the probability that the wind turbine
breaks down?
(b) On a particular day, the operator finds out that the wind turbine broke down.
What is the probability that it is stormy on that day?
(c) Suppose that the operator acquires two turbines that are located in a same
geographical area. If the first turbine breaks down on a particular day, what is the
conditional probability that the second one also breaks down on that day?
(d) Suppose the operator has five turbine that are co-located. On a particular day,
three out of five turbines break down. What is the probability that it is stormy on that
day?

Answer 1