Eudaemonic Pie, Inc. sells computers which predictthe outcome ofa spin ofa roulette wheel. Ifsomeone enters the position of the ball and the approximate speed of the wheel at a given instant in time, the computer will tell you whether to bet on "red," "black," or "green." Normally, red, black, and green arise as the outcomes of any given spin with probabilities 18/38,18/38, and 2/38, respectively. The company rigorously tests their computer system and finds that given the outcome, the probabilities of each computer reading are as follows.
At the roulette table where you are sitting, $10 bets are taken for each spin, and you can stake your bet on the outcome being red, black, or green. The payoff matrix is as follows.
You always have the option not to place a bet.
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