Perform all of the following in a single Mathematica notebook. Use what we discussed in class: to

estimate the probability that some event occurs, perform many trials, and estimate the probability as

probability = (number of times the event occurs)/(number of trials).

To estimate the expected value of some random process, perform many trials, and estimate the expected

value as

expected value = (sum of all outcomes)/ (number of trials).

Possible useful functions: Table, Length, Total, Count, N, RandomInteger, DeleteDuplicates, Histogram.

1. Perform the following experiment 1000 times: roll 3 six-sided dice and add their values. Put the

outcomes in a list called addDiceList. Use Historgram to view the distribution of the outcomes.

2. Perform the following experiment 1000 times: roll 3 six-sided dice and multiply their values. Put

the outcomes in a list called multiDiceList. Use Histogram to view the distribution of the outcomes.

3. Consider the following random process: roll 3 six-sided dice and add their values. Defifine a variable

probSumIs10 that estimates the probability that 10 is produced by this process. (Use enough trials so

that probSumIs10 looks the same up to 2 decimal places.)

4. Consider the following random process: choose 3 random numbers from 1 to 10 (repeats are allowed)

and then select the biggest of those 3 numbers. Defifine a variable called bigThree in Mathematica that

estimates the expected value of this process.