CCSS Honors 2.3 Example 3

Jackson has 2 number cubes numbered 1–6. He rolled both cubes 30 times and recorded the results. (See the Empirical results table shown in the applet.) Based on Jackson’s results, what is the empirical probability that he will roll a sum that is a prime number if he rolls the number cubes one more time? What is the expected value of this next roll based on empirical probability? Compare your results to the theoretical probability that he would roll a prime number on his next roll and the expected value of his next roll based on theoretical probability.
1. Create a frequency table of the possible sums for rolling two number cubes.
2. Use the results to create a probability distribution table.
3. Find the empirical probability that Jackson will roll a sum that is a prime number if he rolls again.
4. Find the expected value of Jackson’s next roll.
5. Find the theoretical probability distribution.
6. Find the expected value of Jackson’s next roll according to the theoretical probability.
7. Compare the empirical and theoretical probabilities of rolling a prime number, and compare the expected values of the next roll based on empirical and theoretical probabilities.