Chapter 11.3, Problem 4A

Solution

(a)

To compare: The graphs of the theoretical and experimental probabilities of sum on two dice and explain if the dice are fair.

Given:

The graph of theoretical probability is shown below

  

The graph of experimental probability is shown below

  

Comparison:

The graphs of theoretical probability and experimental probabilities are slightly different. The experimental probabilities are not equally likely but approximately close to theoretical probabilities. The overall sum of all probabilities is one. So it can be said that dice rolled to calculate experimental probabilities are considered to be fair.

(b)

To explain The differences in both theoretical and experimental probabilities.

Comparison:

The theoretical probabilities for a number on dice is always $\frac{1}{6}$ , and is equally likely. The dice are rolled and the outcomes are noted to calculate the experimental probabilities. The experimental probabilities are close enough to theoretical probabilities but there exists a slight difference between them, so differences are observed in their graphs. As the number of total trials increases the experimental probabilities will be more close to the theoretical probabilities.