Problem
The table shows the results of rolling a fair six-sided die. Complete parts (a) through (d) below. \begin{tabular}{|c|c|c|c|} \hline $\begin{array}{c}\text { Outcome on } \\ \text { Die }\end{array}$ & $\begin{array}{c}\text { First 100 } \\ \text { Trials }\end{array}$ & $\begin{array}{c}\text { Second 100 } \\ \text { Trials }\end{array}$ & $\mathbf{5 0 0}$ Trials \\ \hline 1 & 20 & 19 & 75 \\ \hline 2 & 22 & 20 & 84 \\ \hline 3 & 15 & 22 & 85 \\ \hline 4 & 22 & 15 & 74 \\ \hline 5 & 11 & 14 & 90 \\ \hline 6 & 10 & 10 & 92 \\ \hline \end{tabular} (a) Using the table, find the empirical probability of rolling a 6 for the first 100 trials. The empirical probability of rolling a 6 for the first 100 trials is (Round to two decimal places as needed.)
Solution
Step 1 ：The empirical probability of an event is calculated by dividing the number of times the event occurred by the total number of trials. In this case, the event is rolling a 6 and it occurred 10 times in the first 100 trials.
Step 2 ：So, the empirical probability is \(\frac{10}{100} = 0.1\) or 10%.
Step 3 ：Final Answer: The empirical probability of rolling a 6 for the first 100 trials is \(\boxed{0.1}\) or \(\boxed{10\%}\).
