How far apart two dice land
Two fair dice are rolled. Find the expected value of the absolute difference between the two numbers.
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
For each from 0 to 5, count the outcomes where the difference is .
A difference of happens for ordered pairs with the first die higher, and as many with the second die higher.
h
s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. Count the 36 outcomes by the size of the difference.
Step 1. The difference is 0 in 6 outcomes, and for it is in outcomes: 10, 8, 6, 4, 2.
Step 2. that is .
A comparison. , and the expected maximum is while the expected minimum is ; their difference is again . The expected minimum, about 2.53, is larger than the expected difference.