Chapter 11, Problem 38E

To determine

To Explain: that how likely it is that each individual would be associated with someone other than the individual with whom he or she has come.

Explanation of Solution

There is required to colleagues and, using the following steps, it can simulate:

Step 1

Choosing each player is a component.

Step 2

There is required to produce random digits from 0 to 9 for simulation. Let 1-4 represent the selected four teams, and let 5-9 and 0 disregard the digits.

Step 3

The trial consists of generating a random number sequence that represents the order in which the selection was made.

Step 4

Whether or not digit produced in sequence corresponds to the corresponding digits in sequence 1234 is the answer variable.

Step5

There is required to run the process of simulation with trial numbers. By using random number generators, it produces random numbers using the following steps:

1) As per our needs, add random numbers.

2) Depends on random digits between 0 and 9

3) Press the Submit key.

Step 6

Trial Number	Component Outcomes	Three pairs
1	91616180234	yes
2	147541214	no
3	854756	no
4	9128071734	yes
5	633	no
6	415702	no
7	172957193974	yes
8	15192538857890664	yes
9	12783314	yes
10	917985917823272124	yes
11	3265498431	no
12	99481948	no
13	168949849	no
14	41698494	no
15	16516848	no
16	8468469496	no
Total		6

There is required to find the percentage of the second team being simulated:

  $\begin{array}{c}secondteam=\frac{totalnumberofsuccess}{totalnumberoftrials}\times 100\\ =\frac{6}{16}\times 100\\ =37.5\%\end{array}$

37.5 percent of the second teams are

Step 7

Based on the simulation, it can infer that all participants are supposed to be paired with someone other than someone with whom they decide to take 37.5 percent of the time as the party's responsible variable.