Problem
rolled a number cube 1000 times and got the following results. \begin{tabular}{|l|c|c|c|c|c|c|} \hline Outcome Rolled & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Number of Rolls & 159 & 173 & 132 & 172 & 182 & 182 \\ \hline \end{tabular} wer the following. Round your answers to the nearest thousandths. (a) From Kira's results, compute the experimental probability of rolling a 3. (b) Assuming that the cube is fair, compute the theoretical probability of rolling a 3. (c) Assuming that the cube is fair, choose the statement below that is true. With a large number of rolls, there might be a difference between the experimental and theoretical probabilities, but the difference should be smalt. With a large number of rolls, there must be a large difference between the experimental a theoretical probabilities. With a large number of rolls, there must be no difference between the experimental and Explanation Check
Solution
Step 1 ：The problem provides the number of times a 3 was rolled and the total number of rolls. A 3 was rolled 132 times out of 1000 rolls.
Step 2 ：The experimental probability of rolling a 3 can be calculated by dividing the number of times a 3 was rolled by the total number of rolls.
Step 3 ：Using the formula for experimental probability, which is \(\frac{number\ of\ successful\ outcomes}{total\ number\ of\ outcomes}\), we substitute the given values into the formula.
Step 4 ：Substituting the given values into the formula, we get \(\frac{132}{1000} = 0.132\).
Step 5 ：Thus, the experimental probability of rolling a 3 is \(\boxed{0.132}\).
