The CCBC air conditioning behind Baltimores powers much of the Quad area.There are four identical heat exchangers, three main ones and one back-up.Each exchanger has a probability of failure of 0.10 and they fail independently of each other.Students stay cool (in warm weather) as long as two heat exchangers are currently operating.Let X be a random variable representing the number of heat exchangers that fail.Show all work.

a) Make table showing all the possible values for X and the probability for each value

b) Find the expected value for X, the number of heat exchangers that are currently working.

c) Sketch a probability distribution histogram for the above probability distribution table.

d) Find the probability that the students are cool (that is to say that two or more heat exchangers are operating)