Predicting vs. Observing Probability Examples Page 1

A die was rolled 50 times. These are the results:

6 5 4 5 4 1 3 4 2 6 2 6 1 6 6 4 2 4 5 5 1 1 1 5 3
3 3 1 5 3 6 1 4 1 4 2 3 3 1 2 6 6 4 3 6 6 5 4 2 2

a) What is the experimental probability of rolling each number? 

b) And how do these compare to the theoretical probabilities?

a) Out of fifty rolls of the die:

1 appears nine times; 2 appears seven times; 3 appears eight times; 4 appears nine times; 5 appears seven times; and 6 appears ten times

Thus, the experimental probability is as follows:

b) Now let's compare these to the theoretical probabilities. Each number is equally likely to be rolled, so each has a theoretical probability of ⅙ or about 16.7%. The experimental probabilities are close to this; some are slightly higher and some are slightly lower.