Simulated Experimental Coin-Toss Data (2) submitted by: Jeff LeMieux, June 2003 This narrative describes how I use my javascript tool, cataloged in the Math Tools digital library, in the classroom. Course: Math 7 Topic: Probability, Experimental Probability Resource type: JavaScript Resource location: http://www2.whidbey.net/ohmsmath/webwork/javascript/23coints.htm Math Forum catalogue entry: http://mathforum.org/mathtools/tool.html?rc=tool&new_id=789 Story:  The description of independent versus dependent events is often one which requires students to rethink their current concepts. One of these problem areas in probability is the idea of causality versus probability. Too often people think that thr probability of an event in some way affects their chances - as if probability somehow guarantees a result. (e.g., if there is a probability of 1/2 that a coin will land on heads, and it does land on heads, then the next flip will be tails). One way to deal with this misconception is to ensure an understanding of the difference between an independent and a dependent event. Coin tossing is a decidedly independent event. Students can usually see that what is flipped with one coin does not influence what is flipped with another coin. What is not so clear is whether this remains true when two or three (or more) coins are tossed simultaneously, or to put it another way, are the probabilites different when you flip one coin three times or three coins once. This script serves as a followup to the "cointoss" script which flips one coin. The two scripts can be used to compare the simulated results for a large number of experiments. Where and how I used this: This script is first used in an exercise dealing with counting outcomes. Students can list all of the possible outcomes for the two-coin and three-coin scenario and compare their predictions for the possibilities of various combinations. This script purposely does not give totals so that the students can more actively participate in the 'experiment.' The other use is described above - is there a difference in probabiities between flipping one coin twice or two coins once. Send comments to Jeff LeMieux at tackweed@whidbey.net Jeff LeMieux June 2003 http://www2.whidbey.net/ohmsmath