Question

An octahedral die is a die with 8 sides number 1 through 8 all equally likely to turn face up. What is the expected value of a

single roll of this die?

3. 50

4. 50

4. 25

4. 00

Answer 1

(b) 4.50

Explanation:

You want the expected value of a single roll of an 8-sided die.

Expected value

The expected value of a roll is the sum of the roll values, each multiplied by its probability:

1/8 · (1 + 2 + ... + 8) = 36/8 = 4.50

The expected value of a single roll is 4.50.

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Additional comment

It seems odd that the expected value is not a value that can actually show up. It is the average value expected for a very large number of rolls of the die. (For a 6-sided die, it is 3.5.)

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