```ProbabilityMoss, Laura Willis              South Shore Community Academy                                312-933-8180                           Objectives:

The students will derive a general formula for the probability of a
given event given each possible outcome is equally likely.

Apparatus Needed:

6 dice
30 colored balls (1 each of five different colors)
6 coins
6 paper plate holders
6 plastic cups
6 paper bags
19 ping pong balls (numbered from 0 to 18)

Recommended strategy:

The students were told they had an opportunity to win a prize in
today's class by playing the lottery.  They were to pick a 3 digit
number, a 4 digit number (repeats are allowed) and a combination of 4
numbers from 1 to 18 (no number could be chosen twice).

The students were divided into groups of 3 or 4.  Each group received
a paper bag containing 1 die, 5 colored balls (1 of each  color-blue,
green, yellow, orange and pink), 1 coin, 1 paper plate holder and 1
plastic cup.  Each group had to conduct three experiments.
1.  Flip the coin 50 times into the paper plate holder, record
the results (heads or tails).
2.  Pull a ball from the bag, record its color, replace the
ball and repeat this process a total of 50 times.
3.  Use the cup to shake the die.  Roll the die into the paper
plate holder.  Record the result and repeat the process
60 times.

As a class the data from each experiment was collected.  The students
were asked questions such as:  Were the results of each experiment
what you would have expected?   What would you expect if we were to
repeat the process 1000 times?  10,000 times?  10,000,000 times?

The class then generated the formula for the probability of an event P(E)
P(E) = number of favorable outcomes
number of possible outcomes

Then the class discussed whether or not the formula will tell us
exactly what will happen for a given event.  More examples were
discussed.

The "lottery" ended the lesson.  Students with a knowledge of
permutations and combinations can calculate the probability of each
event.

1       1
P(3 digit number) = --- = ----
103    1000                      1      1P(4 digit number) = --- = ------                    104   10,000P(4 number from 1 to 18) =      1    =     1                                   18!        3060                              14!4!```