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Topic: Experimental/Theoretical Probabilities

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Subject:   RE: Experimental/Theoretical Probabilities
Author: Craig
Date: Jul 7 2005
The best way to help students understand that experimental probability gets
closer to theoretical probability as the number of trials in the experiment gets
large is to let them feel it, first hand.  Have each student toss a coin or roll
a die, say, 25 times, and record the number of heads (or sixes, or whatever) and
the resulting experimental probability.  Have each group of four students
combine their results, so that now the experimental probability is out of 100
trials.  Make a table (on the chalkboard, or, ideally, using a spreadsheet) and
record cumulative results from each group.

For example, group 1 had 43 heads out of 100 tosses, group 2 had 40 heads, group
3 had 52 heads, group 4 had 54 heads... your table should show each group's
experimental probability, and a cumulative list (next to group 2's results,
record 83/200; next to group 3, record 135/300; next to group 4, 198/200, and so
on).  You could even make a chart, showing number of trials on the horizontal
axis and experimental probability on the vertical axis.

If you kept this up for a few days (100 tosses per group, recorded each day...
maybe 5 minutes of class time?) you would see the graph leveling off.  If
technology is available, the spreadsheet or other tools can do lots of
simulations very quickly, and you can really get a feel for the law of large
numbers... but hands-on with middle schoolers will probably help them
understand it better.

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