Chapter 11, Problem 18E

To determine

To Explain: the number of boxes of cereal required to purchase to be pretty sure of getting minimum one and simulation should be minimum 10 trials.

Explanation of Solution

There is ought to find the number of cereal boxes and, using the following measures, it can simulate them:

Step 1

Simulation of the image in one box of cereal is the component.

Step 2

There is required to produce random digits from 0 to 9 for simulation. Let 0 and 1 represent tiger forests, 2-4 represent Beckham and 5-9 represent Serena, and each analysis will consist of generating random numbers until 0 or 1 is generated.

Step 3

The variable responsible is the number of digits produced before the first 0 or 1.

Step 4

There is required to run at least 10 trials of the simulation process. By using random number generators, produce random numbers using the following steps:

1) As per our needs, add random numbers.

2) Depending on random numbers, between 0 and 9

3) Press the Submit key.

Trial Number	Component Outcomes	Trial Outcomes
1	545451	6
2	121	3
3	7878745	7
4	545415878	9
5	545454	5
6	4848	4
7	854854	6
8	8548	4
9	6514	4
10	457	3
Total		51

Let 0 and 1 Tiger Woods random digits, 2-4 Beckham random digits, and 5-9 Serena images random digits. For example, the first random digit 8 means Serena, the second random digit 9 means Serena as well, and the third random digit 0 means Tiger Woods in trial number 1 and gives the total number of results for trial number 1 is 3 and so on.

Step 5

There is required to find simulated cereal boxes that are:

  $\begin{array}{c}Boxesofcereal=\frac{totalnumberofdigitgenerated}{totalnumberoftrials}\\ =\frac{51}{10}\\ =5.1=5boxesofcereal\end{array}$

There are 5 boxes of Tiger Woods cereal.

Step 6

It is fairly clear, based on the simulation, that we need to buy 5 boxes of cereal to be pretty sure of having at least one.