  A number cube has six sides. Each side is numbered, one through six. If we roll
one cube, one is as likely to come up as six. We say the probability of getting
a one, two, three, four, five or six is one out of six in every case. Each number
is equally likely to come up.

The situation is very different for a pair of number cubes. If we roll a pair of
number cubes and add them together the possible combinations are two, three, four,
five, six, seven, eight, nine, ten, eleven, and twelve. A shorthand way of writing
these possible outcomes is the set= {2,3,4,5,6,7,8,9,10,11,12}. If roll a pair of
dice many times we would not expect a two to come up as many times as a six or an
eight. Why? Take a look at the table below. It lists all the ways two cubes can
be arranged.   Please note that there are 6 ways to get a 7 but only 1 way to get a 2. If we roll
the dice many times, we would expect on the average to get many more sevens than
twos.

All together there are 36 possible outcomes. Count them in the table above. The
probability of getting a 2 is only one out of thirty-six or 1/36, but the probability
of getting a 7 is six out of thirty-six or 6/36. We have six times as many chances
f getting a seven than we do a two. If we throw a pair of dice a few times this
pattern may not be very obvious. We need to perform this experiment many times
to see the pattern. That’s where a computer program will help save us time.