Question

. In a tennis serve, a player has two opportunities to put the ball into the game. If the player fails, the two consecutive attempts the player lose the point. Rafael Nadal is playing in a single point for Roland-Garros Championship. He has won the coin toss and elected to serve. If he tries a hard serve (independently if it is the first or second attempt), his probability of getting the serve into play is 0.55. Given that the hard serve is in play, he has .65 chance of winning the point. If he tries a soft serve, his probability of getting the serve in play is .95, but if the soft serve is in play his probability of winning the point is only .50. Assume final rewards as 0 or 1 if he loses or wins the point a) Write the decision tree b) What is the optimal decision the maximize the probability of get a point

Answer 1

a) The decision tree will be:

For example, the top right branch corresponds to winning a hard serve which is in play, while the branch just below that corresponds to losing a hard serve which is in play.

b) For any type of serve, the probability of winning a point will be the product of getting the serve in multiplied by the probability of winning that point when the serve is in.

So, for the hard serve, the probability of winning = 0.55 * 0.65 = 0.3575.

And, for the soft serve, the probability of winning = 0.95 * 0.5 = 0.475.

So, to maximize the probability of winning the point, the optimal decision will be to make a soft serve.