Chapter 11, Problem 37E

To determine

To Explain: How possible it is that any individual would be associated with someone other than the individual with whom he or she has come to the group.

Explanation of Solution

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

Step 1

Each player is an element.

Step 2

There is required to produce random digits from 0 to 9 for simulation. Let the first few couples be represented by 1-2.

The first couples account for 3-4. The first couples account for 5-6. 7-8 reflects the first spouses and the first spouses We need to ignore 9 and 0 here.

 Step 3

The trials consists of producing random digits, ignoring repeats and sorting them into two pairs until pairs are generated representing the first three teams.

Step 4

The response variable is even if there isn't a pairing other than 1-2, 3-4 for each simulated team. Five-six or seven-eight.

 Step 4

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.

Trial Number	Component Outcomes	Three pairs
1	5726305412	yes
2	147541214	no
3	854756	no
4	787403914766095	yes
5	633	no
6	415702	no
7	145398206	yes
8	83892509277958800000	yes
9	12056123627711100000	yes
10	350782	yes
11	3265498431	no
12	99481948	no
13	168949849	no
14	41698494	no
15	16516848	no
16	8468469496	no
Total		6

Phase 5 — Step 5

There is required to find the percentage of teammates that are simulated:

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

The number of teammates is 37.5%.

Phase 6 — Step 6

Based on the simulation, we 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 component.