Question

Suppose that a pair of 7 sided dice is tossed. What is the expected value of the sum?

Answer 1

The expected value of the sum when rolling a pair of 7-sided dice is 8.

Step-by-step explanation:

When rolling a pair of 7-sided dice, each die has numbers 1 through 7 on its faces. To find the expected value of the sum, we need to calculate the average of all possible sums.

The first die can have 7 possible outcomes, and for each outcome, the second die can also have 7 possible outcomes. This gives us a total of 7*7=49 possible outcomes. The sums of these outcomes range from 2 (1+1) to 14 (7+7).

To find the expected value, we multiply each sum by its probability and sum them up. Since each sum has an equal probability of occurring (1/49), we can simplify the calculation:

Expected value = (2*1/49) + (3*1/49) + (4*1/49) + ... + (14*1/49) = 8

Therefore, the expected value of the sum when rolling a pair of 7-sided dice is 8.

Answer 2

IF such dice exist, and
IF each die is numbered from 1 to 7, and
IF each die is fair

then

expected value of each die is 7/2=3.5, and
by the rule of sum of random variables,
E[x]+E[y]=E[x+y],
then
expected value of the sum is 3.5+3.5 = 7.

Note: the platonic solids (convex regular polyhedrons) that can be used as fair dice are
tetrahedron (4 faces)
hexahedron (6 faces)
octahedron (8 faces)
dodecahedron (10 faces)
icosahedron (20 faces)
All of these dice exist in the market.