Question

A tennis player has two chances to get a serve into play. If the first serve is out, the player serves again. If the second serve is also out, the player loses a point. Here are the probabilities based on four years of Wimbledon Championship: P(1st serve in) = 0.59, P(win a point|1st serve in) = 0.71, P(2nd serve in|1st serve out) = 0.86, P(win a point|1st serve out and 2nd serve in) = 0.59.

a. Draw an accurate, properly labeled tree diagram that organizes the probabilities of results of two serves and the outcome (win or loss) for a random selected game.

b. What is the probability that the serving player wins a point in a randomly selected game? Show details.

c. Given that the serving player wins a point in a randomly selected game, what is the probability that his or her 1st serve is in? Show details.

d. Give that the serving player loses a point in a randomly selected game, what is the probability that his or her 2nd serve is in? Show details.

Answer 1

According to the question we have the data and the required is aa diagram

it will be easy for us to solve the answewr using the diagaram

Was this answer helpful?

as ffrom te above question we have a formula

Probability that server wins = P(1st serve)*P(wins| first serve) + P(1st serve out)*P(2nd serve in | 1st serve is out)*P(win point | 1st serve out and 2nd serve in)

from the above question we have all the values required for the formula

so substituting all the values in the above formula we get that :-

= 0.59*0.73 + 0.41*0.86*0.59

solving the above calculation we aget

= 0.6387

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thank you