Why do we need to repeat the simulation several times?
See solution.
Practice makes perfect
We are given information about a simulation conducted in our class. We want to predict the number of boxes of cereal that we need to buy to get all 5 prizes from the boxes. In the simulation, we assume that each box contains a prize and the prizes are randomly and equally distributed.
One of classmates decided to conduct only one trial of the simulation. He concluded that he would need to buy 7 boxes of cereal to collect all the prizes. We can model this outcome by the sequence of numbers, all of which represent the number of prize in the box.
Example Outcome: 1215543
Note that this is only one example of obtaining all 5 prizes in 7 boxes. However, the approach of the classmate is incorrect. We need to repeat the simulation several times, because — in general — the number of boxes we have to buy to collect all 5 prizes will vary.
Trial
Number of Boxes
351312124
9
12254451153
11
322123142324125
15
23154
5
523244245343343422542321
24
We can simulate buying boxes of cereal by generating random numbers between 1 and 5 until we have simulated getting each prize at least once. Let's repeat the experiment 20 more times and write down how many numbers we had to generate until we got all five prizes.
ccccc
9 & 11 & 15 & 5 & 24
18 & 11 & 7 & 15 & 10
22 & 8 & 8 & 16 & 12
13 & 8 & 9 & 17 & 15
18 & 10 & 7 & 23 & 14
Now we will find the average number of boxes needed to collect all 5 prizes. To do so, let's divide the sum of the numbers, 325, by the number of trials. Recall that we performed 25 simulations in total.
Average Number of Boxes [0.5em]
325/25 = 13
Therefore, on average we need to buy about 13 boxes of cereal to get all 5 prizes.
