Tip:
Highlight text to annotate it
X
Welcome to the post class activity for probability, developed as part of the
MTStatPAL project at Middle Tennessee State University.
If you did the in-class activity for probability, you flipped coins and dropped candies on
plates. One goal of the activity was to distinguish between empirical probability,
which is based on observed data, and theoretical probability, which is based on a model of
the experiment. The law of large numbers tells us that as the number of repetitions of an
experiment gets large, the empirical probability gets close to the theoretical
probability.
This animation shows the law of large numbers in action. A fair coin is being flipped
repeatedly. The blue line represents the empirical probability. As the coin is
flipped again and again, the proportion of heads observed changes, so the blue values
change as well. The green line is at the theoretical probability of heads, which is
0.5. This value does not changed with each flip, because the theoretical probability is
based on the model of a fair coin and not on the specific outcomes being observed. As we
increase the number of flips, observe that the blue line eventually gets close to the
green line.
You will also have learned that the models for a coin flip and a candy drop are the same. That
is, the same probability model can be used for many different random experiments.
Finally, you learned the probability rules, that probabilities are numbers
between 0 and 1, and the total probability in the model should be 1.
The experiments that you ran in class had only two outcomes: heads or tails for the coin,
and left or right side of the plate for the candy drop. This presentation will focus an
experiment with more than two outcomes, roulette. Other experiments with more than two
outcomes include playing cards, dropping candy on a plate that is divided into many pieces,
and more serious outcomes in medicine, business, and science.
The casino game of roulette consists of a large wheel that is spun, and a small ball that
is dropped on the wheel. A person wins if the ball falls on the number they have chosen.
There are 38 numbers altogether: 1 through 36, 0, and 00. Half of the numbers 1
through 36 are red while the other half are black. 0 and 00 are green.
Assuming the wheel is fair, what is the probability of getting any one specific number? Since