Your regular tennis partner has made a friendly wager with y

Your regular tennis partner has made a friendly wager with you. The two of you will play out one point in which you can serve. The loser pays the winner $100. If your first serve is not in play, you get a second serve. If your second serve is not in play, you lose the point. You have two kinds of serves: a hard one and a soft one. You know that your hard serve is in play 65% of the time and, when it is in play, you win the point 75% of the time. You put your soft serve in play 80% of the time, and when it is in play, you win the point 50% of the time. [Note: You will need a second serve only if your first serve is not in play. You may use different types of serves in two serves.]

5.3.a Draw a decision tree for this problem. [Draw a tree on your own before checking the answer on the next page.]

5.3.b (1 pt) Calculate the expected point for each possible strategy. Use expected point as your decision criterion. Should you accept the wager? If so, what is your strategy? (Choose the best answer.) A) Do not accept the wager. B) Accept the wager. Use hard serve all the way.

C) Accept the wager. Use soft serve all the way.

D) Accept the wager. Use hard serve first. If the first serve is not in play, then use soft serve.

E) Accept the wager. Use soft serve first. If the first serve is not in play, then then use soft serve

Solution

a)

b) epected of wining with soft = 100*0.8*0.5 = 40 ( 100 because winning amount is 100)

expected of wining with hard = 100*0.65*0.75= 48.75

if i have to make a decision then i will accept the wager and choose a hard serve