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Three dice are rolled. What is the probability that the sum is 15 or more? …
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Three dice are rolled. What is the probability that the sum is 15 or more? Estimate it with 300 000 simulated rolls, and compare it with the exact answer. (By symmetry, the number of triples with a sum of 15 or more is the number with a sum of 6 or less, and there are 20 of them out of 216.)
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Make a table of 300 000 rows and 3 columns of dice, add along each row, and find the share of rows with a sum of 15 or more.
Check. The simulation gives 0.0930 and the exact value is . The difference, 0.0004, is about the size that we expect for 300 000 trials: .
Answer: about 0.093. The exact probability is 20/216 = 0.0926.
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