Activities for
Empirical Probability
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No dice handy?

Group students together to investigate empirical probability.
Any of the problems from this section may be used to create experiments.

 

Possible experiments with fair, unbiased objects may include:

1.
What is the probability of rolling a 3 with one die?

Students can work independently or in groups to gather data depending upon the number of die available.

2.
What is the probability of drawing a king from a deck of cards?

Students work in groups to gather data.

 
3.
What is the probability of drawing a red marble from a bag containing 3 red marbles and 5 blue marbles?

Students work independently or in groups depending upon the number of manipulatives.  If marbles are not available, colored slips of paper also work well.

4.

What is the probability of tossing a tail using a penny?

Students work independently or in groups to gather data.

 

5.
A box contains 20 slips of paper.  Five of the slips are marked with a "X", seven are marked with a "Y", and the rest are blank.  The slips are well mixed.  Determine the probability that a blank slip will be drawn without looking in the bag on the first draw.

Have students determine the probability theoretically and then have each conduct the experiment with ten trials and see how close the empirical  probability was to the theoretical probability.  Combine data from all students in the class to see if a larger number of trials will result in an empirical probability that more closely resembles the theoretical probability. 
                                                                       

For each activity listed above, set the minimum number of trials:
For example:  minimum number of trials = 100

Have students tabulate information as it is gathered in some organized manner:

Group member Number of 3s. Number of rolls
Sue 9 30
Joe 12 30
Wally 18 40

You may also wish to have students compare their results with the theoretical probability, and write a short paragraph explaining the comparison.

 

Possible experiments with biased objects:

1.

Glue a dime to a nickel to create a weighted coin.  Be sure the weighted coin has a head and a tail.  What is the probability of tossing a head?

 

2.

Toss a Dixie cup (a paper cup).  It may land in one of three positions:  on its top, on its bottom, on its side.  What is the probability of the cup landing on its top?