Chapter 13, Problem 18SGR

To determine

Describe how you would use the geometric probability model to design a stimulation.

Explanation of Solution

Given:

M scores 35% of the goals his team earns in each water polo match.

Calculation:

Step 1 :

Possible Outcomes	Theoritical Probability
M scores goals	35%
M does not score goals	(100-35)% = 65%

Step 2:

The simulation will consist of 100 trials.

Step 3:

We can use a spinner divided into two sectors, one containing 35% of spinner’s area and the other containing 65% of spinner’s area .Find the measurement of central angle of each sector.

M scores goals = $35\%\text{ of }360°=126°$ : Blue sector

M does not score goals = $65\%\text{ of 360}°\text{ = 234}°$

: Yellow sector

Step 4:

A trial means one spin on the spinner , represents goal scored by M or not .

A successful trial will be M does not score goal and a failed trial means M scores a goal .

The simulation will consist of 100 trials.

Perform 100 trials and record the result.