5. David made up a set of two 6-sided dice with these numbers on them.
16 marks]
IF
-3, -2, -1, 0, 1, 2
Suppose the pair of dice is tossed.
a. list all the ways to get a sum of -4
b. list all the ways to get a sum of 0.
c. list all the ways to get a sum of -1
d. If the dice were tossed 100 times, which sum would be the most popular? Explain your

a. 3 ways: -3 and -1; -2 and -2; -1 and -3

b. 5 ways: -2 and 2; -1 and 1; 0 and 0; 1 and -1; 2 and -2

c. 6 ways: -3 and 2; -2 and 1; -1 and 0; 0 and -1; 1 and -2; 2 and -3

d. A sum of -1 would (probabilistically) be the most popular. There are 36 (6 x 6) possible outcomes every time you roll two 6-sided dice. In this case, the possible outcomes are:

-6: 1 way

-5: 2 ways

-4: 3 ways

-3: 4 ways

-2: 5 ways

-1: 6 ways

0: 5 ways

1: 4 ways

2: 3 ways

3: 2 ways

4: 1 way

So -1 is the most likely sum since it can be rolled 6 different ways, which is more ways than any other sum. A sum of -1 will be rolled 6/36 (or 1/6) of the time.