Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win \(\$ 1\) million. The contestant picks from four hidden windows. Behind each is one of the following: \(\$ 150,000, \$ 200,000\), \$1 million, or a "stopper."

a. If the contestant picks the window containing \(\$ 150,000\) or \(\$ 200,000\), the contestant is asked whether he or she wishes to quit or continue. Suppose a certain contestant has picked both the \(\$ 150,000\) and \(\$ 200,000\) windows. Mathematically speaking, should the contestant pick "one more time"?

b. Suppose you owned a \(\$ 350,000\) home free and clear; would you gamble it on a \(50 / 50\) chance to win \(\$ 1,000,000\) ? According to the mathematical expectation, what should you do? Discuss.