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Roll two dice 6000 times, with the seed 3…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Roll two dice 6000 times, with the seed 3. Count how many times each sum from 2 to 12 comes up, and show the sum that comes most often. Which sum do you expect, and why?
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. There are 36 equally likely pairs. The sum 7 has the most pairs: (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1), which is 6 of 36. The sum 2 has only one pair, (1,1). So we expect 7 to be the most common, with about 1000 of the 6000 rolls.
Check. The counts rise from the sum 2 (about 167) to the sum 7 (about 1000), and then fall again to the sum 12. The shape is a triangle.
Answer: The sum 7. It has six ways out of 36. (The exact counts depend on the seed.)
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