Chapter 13.5, Problem 21PPS

(a)

To determine

Draw a probability tree that shows each outcome.

Explanation of Solution

Given:

A double fault in tennis is when the serving player fails to land their serve “in” without stepping on or over the serving line in two chances.K’s first serve percentange is 40% , while her second serve percentage is 70%.

Calculation:

The probability tree is :

(b)

To determine

Find the probability that K will double fault.

Answer to Problem 21PPS

0.18 or 18%

Explanation of Solution

Given:

A double fault in tennis is when the serving player fails to land their serve “in” without stepping on or over the serving line in two chances.K’s first serve percentange is 40% , while her second serve percentage is 70%.

Calculation:

The double fault is back to back faults , and given probabilities of serves in 1^st and 2^nd serving are 0.4 and 0.7 respectively.

So, the probabilities of faults in 1^st and 2^nd serving are (1-0.4 =) 0.6 and (1-0.7 = ) 0.3 .

Hence the probability that K will double fault = P(F,F) = $0.6\times 0.3=0.18$

(c)

To determine

Design a simulation using a random number generator that can be used to estimate the probability that K double faults on her next serve.

Explanation of Solution

Given:

A double fault in tennis is when the serving player fails to land their serve “in” without stepping on or over the serving line in two chances.K’s first serve percentange is 40% , while her second serve percentage is 70%.

Calculation:

Step 1 :

From part (a),

Possible Outcomes (2 serving)	Theoritical Probability
Serve	0.4
Fault,Serve	0.42
Fault, Fault	0.18

Step 2:

Assume that the servings will fall into these three categories.

Step 3:

Use a random number generator on your calculator.Use the ten integers 0-9 to accurately represent the probability data.The actual numbers used to represent the outcome does not matter.

Possible Outcomes (2 serving)	Represented By
Serve	0,1,2,3
Fault,Serve	4,5,6,7,8
Fault, Fault (double fault)	9

Step 4:

A trial means two servings and recording the serve or fault. The simulation will consist of 20 trials.