Consider using a spinner to perform a simulation. Then remember to repeat the simulation several times.
See solution.
Practice makes perfect
We are given information about a grocery store gifting scratch-off tickets to customers who spend over $50. Each ticket consists of one type out of 3 possible discount offers that are randomly and equally distributed among the tickets. We can simulate getting particular discount offers using a spinner.
Let's spin the spinner and write down the results in a frequency table. We should stop spinning when we have simulated getting each discount at least once. Keep in mind that this is just one possible simulation we can do to obtain the frequency table.
Simulation of Discount Offers
Discount
Tally
Frequency
1
/ /
2
2
/
1
3
/ / /
3
This trial indicates that we would expect to spend over $50 in the grocery store 6 times in order to get all 3 discount offers. Now we will repeat the simulation 29 more times and note each number of times before we get all 3 discount offers. We will also include the first result.
cccccc
6 & 9 & 3 & 3 & 4 & 3
4 & 3 & 4 & 3 & 6 & 5
4 & 5 & 4 & 4 & 5 & 4
5 & 3 & 7 & 7 & 6 & 3
6 & 9 & 4 & 5 & 5 & 6
Next, we will calculate the average number of scratch-off tickets we would need to collect all the discounts. To do so let's divide the sum of the results, which is 145, by the number of trials. Recall that we performed 30 simulations in total.
Average Number of Tickets [0.5em]
145/30 ≈ 5
Therefore, on average, a customer needs to spend more than $50 in a grocery store about 5 times to get all 3 discount offers.
