A teacher randomly assigns students new seats each week. We want to find the average number of weeks before a student is assigned the same seat for two weeks in a row. We are not given the exact number of seats in the class, so we will assign an arbitrary value for it.
Numberofseatsinclass=20
We will assume that there are 20 seats in class. We are asked to find how long on average will it take for a student to be assigned the same seat two weeks in a row. To do that, we will simulate assigning seats to one specific student.
👦←TomWewillsimulateassigningseatstoTom.
Let's perform our first simulation together! First, on a graphic calculator, press MATH and go to the PRB column. Then, choose the fifth option, randint(.
Now press ENTER. We want to use the randInt( function to generate random numbers — which represent the seats — from 1 to 20 about 100 times. The calculator will do that for us if we type in randInt(1,20,100). The output should look like the one in the following picture. Since the process is random, your numbers will be different.
In our case, we can see that Tom was assigned seat 3 in the first week, seat 14 in the second week, seat 20 in the third week, and so on. Let's write down this information in a table.
Week
Seat
1
3
2
14
3
20
4
13
5
7
6
2
7
20
8
4
9
8
10
3
11
5
12
18
13
8
14
3
14
12
15
13
16
2
17
5
18
5
In the first simulation, Tom was assigned the same seat two weeks in a row after 18 weeks! Now we can repeat this process 9 more times. We will show the results of all of the simulations in a table.
Simulation
Number of Weeks After Tom Got the Same Seat Two Weeks in a Row
1
18 weeks
2
40 weeks
2
11 weeks
3
42 weeks
4
9 weeks
5
6 weeks
6
89 weeks
7
14 weeks
8
3 weeks
9
70 weeks
10
5 weeks
Now let's calculate the average number of weeks.
AverageNumberofWeeks=1018+40+11+…+70+5≈28
Based on our simulations, we found that the average number weeks before a student is assigned the same seat two weeks in a row is about 28 weeks. Since the simulations were random, your answer might be different.
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