On each point in tennis, a player is allowed two serves. Suppose you get your fi

Question

On each point in tennis, a player is allowed two serves. Suppose you get your first serve in about 75% of the time. When you get your first serve in, you win the point about 80% of the time. If you miss your first serve, your second serve goes in about 90% of the time. When this happens, you win the point on your second serve about 35% of the time.

a. Find the probability that you win a point when serving.

b. If you know you won a point while serving, what is the probability that you made it on your first serve?

Explanation / Answer

a) Probability of winning a point on serving

= (0.75 * 0.8) + (0.9 * 0.25 * 0.35)

[As the first term of (0.75 * 0.8) is the probability of winning a

point in the first serve and the second term is the probability of

winning a point in the second serve multiplied by the

probability that the first serve will be missed]

= 0.67875. (Ans).

b) The probability that a point is won on first serve

= (0.75 * 0.8) / 0.67875 = 0.8840. (Ans).

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.