A law firm takes cases on a contingent fee basis. If the case goes to trial, the firm expects to earn $25,000 as part of the settlement if it wins and nothing if it does not. The firm wins one-third of the cases that go trial. If the case does not go to trial, the firm earns nothing. Half of the cases do not go to trial. Be sure you add the appropriate units.
(a) Define a random variable to model the earning of taking a case of this type.
(b) What is the expected value of such a case to the firm?
(c) What is the standard deviation of the earnings?