Chapter 8.1, Problem 87E

In Problems $87\text{-}90$, several experiments are simulated using the random number feature on a graphing calculator. For example, the roll of a fair die can be simulated by selecting a random integer from, and $50$ rolls of a fair die by selecting $50$ random integers from $1\text{ to }6$ (see Fig. A for Problem $87$ and your user's manual).

From the statistical plot of the outcomes of rolling a fair die $50$ times (see Fig. B), we see, for example, that the number $4$ was rolled exactly $5$ times.

(A) What is the empirical probability that the number $6$ was rolled?

(B) What is the probability that a $6$ is rolled under the equally likely assumption?

(C) Use a graphing calculator to simulate $100$ rolls of a fair die and determine the empirical probabilities of the six outcomes.