Thursday, April 7, 2011

What are the chances of a “Pig Out”? Part II

Last post, I shared with you the first half of an article I wrote with Dr. Mary Richardson (here is another article I wrote with Mary addressing fair games). Learners have just predicted the chances of rolling a "Pig Out" in the popular Pass the Pigs game. They are now ready to explore the experimental probability associated with this question.

The Activity (continued)
After learners share their subjective estimates, they are ready to test them by developing an experiment, as described on the Activity Worksheet.  In the activity, learners create possible plans for determining an estimate of the chances of a “Pig Out”.  Once plans have been suggested, the class discusses the plans, agrees on a plan to utilize, and carries out the plan.  One possibility would be to have each pair of learner toss the pig dice several times in order to see how often a “Pig Out” occurs. For example, within each pair, the following tasks are assigned:  one member tosses the pigs; and the other member records whether or not the pigs landed in the “Pig Out” position.  After one learner completes ten trials, the students switch tasks and ten more trials are conducted.  This provides partners with a total of twenty trials that can be used in determining an experimental probability.

Once the learners have conducted the experiment, we ask them to refine their original guesses.  When asked how they could be more certain of the probabilities, most respond that a longer experiment (more tosses) would result in more certainty.  However, they recognize that it is unrealistic for each of us to toss the pigs a very large number of times.  Instead, we decide to use the results from the entire class to get a better estimate for the probability.  We draw a number line on the whiteboard.  Each learner writes his/her own result from their tosses on a sticky note and posts the note appropriately on the line in order to form a dot plot.  After we have discussed the data for the whole class, everyone makes a new estimate for the probability.

Learners are asked to share their new probability estimates.  Most learners select the class median or class mode as their new estimate.  We estimate that a “Pig Out” is rolled one time in every five rolls.  Of course, differences in desktops, and the very nature of the experiment may produce varying results.

The important concept in this activity is that one cannot simply count outcomes for every object and assign a theoretical probability to any given outcome.  By exploring objects that cannot be assigned theoretical probabilities, learners seem to have a greater understanding of when a theoretical probability can be assigned.  Furthermore, learners recognize the need to generate data in order to obtain experimental probabilities
The exploration did not end there for us. We found several websites dedicated to Pass the Pigs. They contained online versions of the game and data collected in secondary classrooms. We used the data to update our experimental probabilities and look at new questions.

Sadly, the websites we found are no longer, but Wikipedia has data on rolling a single pig 11,954 times. Maybe you could use these to collect your own data to answer your own questions. For example, in order to win the game, you want to know when to pass the pigs. Therefore, the next question we asked was, "How long until we "Pig Out"? We came up with two ways to answer this question but I bet there are more.

1 comment:

  1. I have my class divided into groups, and each group have to come up with a strategy, like: "throw the pigs Y times, unless we have less than X points then we throw Z times more."

    Last day we have a competition with a webcam on the teachers desk and see if we can find a winner. Great fun!