Since there was much less snowfall last year, your income did not cover the cost and expenses of a new truck. A couple of years ago, however, you would have been able to meet your expenses because the number of snowfalls was unusually high.

One of the random variables in this scenario is the number of times you are required to plow a driveway. You investigate the weather patterns from past years and find that the average number of times that there is snowfall that requires plowing (a snowfall of two inches or more) is seven per season.

You've noticed that the number of snowfalls in a particular season varies from 2 to 12, similar to the sum of the outcomes of rolling two fair dice. In other words, the probability of getting a particular number of snowfalls in a given year mimics the probability of getting that same number when two fair dice are rolled.

The chance of having 7 snowfalls in any season is relatively high, while the chances of receiving 2 or 12 snowfalls are appreciably lower. So, you can use two dice to model the number of snowfalls, on average, over the coming seasons. If you model it well, you can find out how much revenue to expect.

Activity

You use two dice and randomly generate a sequence of numbers to simulate the number of times you would have to plow.

Question 1

What is the probability of getting each outcome when rolling two dice?

Outcome	Probability
2
3
4
5
6
7
8
9
10
11
12

Using the probabilities you found in the previous part of this activity, calculate the total income you'll get for the number of plowings from each customer.

Outcome	Probability	Total Income = Outcome Probability 75
2
3
4
5
6
7
8
9
10
11
12

Question 4

Find the expected value per customer using your table.

question 5: You are thinking of getting a five-year loan to buy a new truck. If you do, your estimated monthly expenses will be $400 for the next five years. What are your five-year estimated business expenses? (You do not need to consider inflation of the interest rate.)