### Some Interesting Things About Dice

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
dice 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 the sum of 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
of 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. Thatâ€™s where a computer program will help save us time.

### Roll The Dice

####
If you roll a pair of number cubes there are several

possible outcomes. They are 2, 3, 4, 5, 6, 7, 8, 9,

10, 11, and 12. Is each one of these outcomes equally

likely, or will some numbers come up more than others?

We could perform this experiment with real dice, but it

would take several hundred trials and that would take

a lot of time tossing, adding, recording and summarizing.

There is an easier way. You can let the computer do the

work for you. All you have to do is tell the computer

how many times you want to toss the dice. The computer

will toss, add, and record, and summarize each event.

This will give you more time for the important job of

looking for the pattern. To get good results start with

a hundred tosses, and then gradually increase the sample

size to ten-thousand. Computers are amazingly fast.

Imagin how long it would take you to toss a pair of dice

10,000 times, and summarize your results.

Copyright 2021, William Johnson