Consider the following:
Three dice are rolled. What is the probability that the sum of the numbers that come up is 7? Complete a spreadsheet to conduct an experiment, and compare the empirical probability to the theoretical probability.
In order to begin, we computed the theoretical probability. We looked at rolling two dice and wrote all the possible combinations. Through this process we found that there were 36 combinations for the two distinguishable dice. Next, we had to consider which of these summed to be seven, six combinations summed to seven. Next, we looked at three distinguishable dice, and found that the total number of possible combinations is 216. The total number of combinations that sum to seven is 15. We did this using the same process as with two dice. The theoretical probability that the sum of the numbers come up as 7 is 15, when three distinguishable dice are rolled.
The spreadsheet simulates 100 rolls. Calculate the experimental probability. What will happen if we record several experimental probabilities and find the average?
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Discuss your results.