## Part 2.
"Tossing" Two Dice by Simulation on the TI-83/84 Calculator

(The
singular of dice is die!)

Earlier
we tossed two actual dice and recorded the results. Now we will simulate the toss of two dice on
our TI-83/84 calculators. How to do it?

randInt(1,6)+randInt(1,6)
ENTER

gives the toss of two dice. (Do you understand why?)

Your
first task is to simulate the roll of two dice 36 times using your calculator,
and to record the sums on a tally sheet. (You may print out a tally sheet in
Part 1 on tossing dice here.)

We
will then compare the probability of getting each sum to our observed frequencies. There is a theorem that says most often, if
we keep rolling, our whole distribution of observed frequencies will come
closer and closer to the theoretical probabilities. This is the meaning
of the statement that "in the limit" the observed frequencies approach the
probabilities.

In
Part 3 we will work on a new amazing program, DICETOSS, that
simulates the roll of two dice in groups of 200 rolls, and plots the
frequencies of their outcomes. We can then actually "see" how our
experimental frequencies approach the theoretical probabilities.

To
help you get your simulated data, there is a shortcut for getting 36 simulated
rolls, and for sorting them so that they are easy to graph:

randInt(1,6,36)+randInt(1,6,36) →L1
ENTER

SortA(L1)
ENTER (this step is optional)

If you
want to know the fractional number of each of the outcomes from 2 to 12,

sum(L1=2)/dim(L1) →A:A►Frac

sum(L1=3)/dim(L1) →A:A►Frac

sum(L1=4)/dim(L1) →A:A►Frac

...

sum(L1=12)/dim(L1) →A:A►Frac

Now on a
tally sheet, graph your frequencies. How
do they compare with the probabilities that you computed in Part 1? How do they compare with the frequencies you
computed from the data you collected by tossing actual dice in Part 1?

Webpage Maintained by Owen Ramsey

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