Question
Serena and Venus are the finalists in the US Open (hypothetically). The winner’s prize is $2
million; the loser gets $400,000. Both tennis stars are aware of a performance-enhancing drug (without bad
side-effects) that
Serena and Venus are the finalists in the US Open (hypothetically). The winner's prize is $2 million; the loser gets $400,000. Both tennis stars are aware of a performance-enhancing drug (without bad side-effects) that could be taken before the championship match. This drug has been banned, but is difficult to detect (each faces a post-match drug test). The penalty for doping in the Women's Tennis Tour is a one- year suspension (with an expected loss of $5 million) Serena knows that she is certain to win if she takes the drug, but Venus remains drug free, and vice versa. When both rivals follow the same strategy each believes that her chance of winning the match is even (50% probability) Each player knows that the probability of being caught by the drug test is 10%, if she does take the drug. Drug test outcomes are independent events. If the winner fails the drug test, she forfeits her prize which is then awarded to the loser (as long as the loser passes the test). If both fail, both forfeit their prizes in addition to suffering the one-year suspension. (10 points) Suppose that neither Venus nor Serena take the drug. What is the mean payoff? (10 points) Suppose that neither Venus nor Serena take the drug. What is the standard deviation of the payoff? (a) (b) (c) (10 points) Suppose that both take the drug, what are the four possible drug-test outcomes? Draw two- (d) (10 points) When both take the drug, what is the probability that at least one player fails the test, (e) way table to illustrate this situation. Fill in the probabilities in this table (10 points) When both take the drug, what is the mean payoff? What is the standard deviation of the payoff?
Explanation / Answer
a) Mean Payoff = 1/2*2-1/2*0.4 =1.2 million
b) Standard deviation = [1/2* [2-1.2]^2 +1/2*[0.4-1.2]^2 ]^0.5=0.8 million
c) FOur outcomes are
P( No one caught)=0.9*0.9=0.81
P( only serena is caught)=0.9*0.1=0.09
P( only venus is caught)=0.9*0.1=0.09
P( Both are caught) = 0.1*0.1=0.01
d) P( At least one pair fails the test) =0.09+0.09=0.18
Please post the other parts individually
