Read all the directions on this assignment before you proceed.

To do this assignment you will need:

1. A pair of 6-sided dice or a dice-rolling app

1. Use the classical probability model to fill in thefirst three columnsof the table and find the probability of rolling each of the numbers 2 through 12 on a pair of two six-sided dice.

Number	# of different possible ways to roll this number	Total # of possible rolls	Classical probability of rolling this number	Expected # of rolls out of 100	Actual # of rolls out of 100	Empirical probability of rolling this number
2		36
3		36
4		36
5		36
6		36
7		36
8		36
9		36
10		36
11		36
12		36

2. Fill in the fourth column of the table by using the classical probabilities you found in part 1 to estimate how many of each number you should expect to roll if you roll a pair of dice 100 times.

3. Roll a pair of dice 100 times and record your results on scratch paper. Use this datato fill in column 5. Then, compute the empirical probability of rolling each number using this data, and fill in column 6.

4. Are the dice you rolled fair dice? Why or why not?

5. Use classical probability, the addition rule, and/or the complement rule to answer the following. SHOW WORK.

1. To win in craps, you need to roll a 7 or an 11. What's the probability of rolling a 7 or an 11?

2. What's the probability of rolling an even number or a multiple of 3? (Note that these outcomes are not disjoint; 6, for example, is both an even number and a multiple of 3.)

3. To get out of jail in Monopoly, you need to roll doubles, i.e. both dice show the same number. What's the probability of NOT rolling doubles?