Experimental Probabilities:  Preliminary Simulations

Experimental Probability

Probabilities help us to predict the likelihood of uncertain occurrences.  Basically, the probability of a particular outcome (e.g. a chip landing in the $10,000 slot) is a number that tells us the relative frequency with which we expect the outcome to occur.  The experimental probability, denoted P(event), that an event will occur is computed by making many repetitions of an experiment and determining the relative frequency that the event occurs, so that P(event) = number of times event occurs / number of repetitions, that is

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Activity:  Have each student (or team of students if the class is large) drop 5 chips.  Record the starting slot, ending slot, and the dollar amounts for each play in the table  (click here to see a sample chart).  Students enjoy the competitive nature of the game, so recording total winnings keeps students interested despite the repetitive nature of the activity.  After each student or team has played, complete the chart to compute the probabilities, based on the cumulative data, of winning $0, $100, $500, $1000, $10000 with a single chip.  This is a great time to ask students why they chose their particular starting slot.  What slot do they think is the best place to start the chip in order to win the big money?  How might we anticipate our winnings if we play with 5 chips?

It is important to observe that experimental probabilities would likely vary from experiment to experiment and it is helpful at this point to discuss what factors might cause variation in the computations (have students to suggest ideas, but make sure that they understand that the number of repetitions in an experiment is a factor).