Theoretical and Experimental Probability
Theoretical Probability

A ratio that compares the number of possible successful outcomes to the total
number of possible outcomes.

Determined by reason or calculation.
Activity
Determine the theoretical probability of obtaining each of the possible sums when rolling
two dice.
Total of
Two Dice
Number of
Combinations
2
1
3
2
Theoretical Probability
Fraction of the
Percent of the
Total Number of
Total (to the
Combinations
nearest percent)
2
1
=
36
18
4
5
6
7
8
9
10
11
12
***Make sure you write all fractions /36 and in lowest possible terms***
Theoretical Probability – Reflection Questions
1) Two dice are rolled 100 times. How many times should the total of the dice be 2?
Explain why.
2) How many times would you expect to roll a total of 8 with 1000 rolls of two dice?
3) The theoretical probability of rolling a total of 7 with two dice equals the sum of
the probabilities of rolling which other numbers?
Theoretical and Experimental Probability
Experimental Probability

A ratio that compares the number of times an event occurs to the total number of
trials or tests.

Determined by experiment.
Activity
Determine experimental probability by rolling two dice 50 times. Record your results in
the table below.
Total of Two
Dice
2
3
4
5
6
7
8
9
10
11
12
Tally
Number of
Times Rolled
Experimental Probability
Fraction of the Percent of the
Total Number
Total Number
of Rolls (in
of Rolls
lowest terms)
Experimental Probability – Reflection Questions
1) How many times did you roll a 5?
2) What is the experimental probability of rolling a total of 5, as a percent?
3) What is the theoretical probability of rolling a total of 5, as a percent?
4) Does your experimental probability match your theoretical probability for rolling a
total of 5?