Use a random number generator to perform a simulation.
See solution.
Practice makes perfect
Myriah rolls two dice and, if the sum of the dice is 6 or less, she will wash the dishes. On the other hand, if the sum is 7 or more, one of her parents will wash the dishes.
We want to design a simulation to estimate the number of days Myriah can expect to do the dishes in a random week. We can do this by using the random number generator in our graphing calculator. To do so, push the MATH button, then scroll right to the PRB menu and choose the fifth option, randInt(.
After choosing this option, enter the minimum and maximum values of the set and the number of trials. In our case, the minimum value is 1 and the maximum value is 6 because this is the range of numbers we can get when rolling a die. Let the number of trials be 60 since we want to have 30 pairs of results. Next, push ENTER.
Let's take a look at a table with the example results of our simulations. We want to look at pairs of numbers, so we will pair off our integer values. We will highlight the pairs that add up a sum of 6 or less.
Results
5,3
4,2
3,5
1,2
5,3
4,2
5,1
3,4
4,5
6,4
6,1
1,2
5,3
6,6
4,6
4,5
5,4
3,2
5,5
1,3
6,5
1,2
2,2
4,3
2,4
6,6
2,2
3,3
4,2
1,3
Using the results from our simulation, we can estimate the number of days Myriah can expect to have to do the dishes. Out of our 30 simulations, 14 resulted in pairs that add up to 6 or less. Let's then compare these two counts to find the probability of Myriah doing the dishes on a given day.
14/30 &= 0.466666 ...
&≈ 0.47
If we multiply this daily probability of doing the dishes by the total number of days in a week, we will get an estimate of how many days each week Myriah can expect to have to do the dishes. Remember, there are 7 days in a week!
0.47 * 7 = 3.29
We found that Myriah can expect to do the dishes on about 3 days each week. Notice that this is only an example solution since different random number tables might result in different solutions.
