2.6 Basic Probability

Experimental Probability

Investigation: toss two thumbtacks and record the results. The possible outcomes are: 2 backs, 1 back and 1 side, 2 sides. NO STABBINGS ALLOWED!

1. Perform 80 trials.
2. Obtain relative frequencies.
3. Pool your results with four other people so that you have the results from 400 tosses.
4. Which gives the more reliable results, your results or the large group results? Why?

Experimental Probability = Relative Frequency

Notation: indicates the likelihood that event A will occur.

Theoretical Probability

In theoretical probability, we calculate as how we expect it will happen based on the total ways A can occur out of a total number of outcomes in the sample space. All of these outcomes must be equally likely.

Investigation: roll a pair of dice and record the results of the sums.

1. Perform 40 trials.
2. Obtain relative frequencies.
3. Pool your results with four other people so that you have the results from 200 tosses.
4. Create a table to record all of the possible outcomes for either dice.
5. What do you expect the probability of rolling a 7 to be from your table? How does that compare to your experiment?

, where A is the set of outcomes that fit your requirement and S is the sample space.

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