WFU Law School
Law & Valuation
2.2.1 Probability Distribution

2.2.2 Expected Return

What is the expected return when we throw two dice? Suppose the number you throw represents the return, and suppose you throw the dice thousands of times. What would you expect your return to be on average? We can compute the expected return for each possible result and then sum these results.

Return
Probability
Weighted expected return
$2
1/36 = 2.8%
$0.056
$3
2/36 = 5.6%
$0.168
$4
3/36 = 8.3%
$0.252
$5
4/36 = 11.1%
$0.555
$6
5/36 = 13.9%
$0.833
$7
6/36 = 16.7%
$1.167
$8
5/36 = 13.9%
$1.111
$9
4/36 = 11.1%
$1.000
$10
3/36 = 8.3%
$0.833
$11
2/36 = 5.6%
$0.611
$12
1/36 = 2.8%
$0.333
Total
36/36 = 100%
$7.00

The expected return? $7.00.

Consider a probability distribution example with less variability -- that is, a distribution with less risk that your returns deviate from the average. This time suppose you are throwing two six-sided dice, but each dice has only three 3's and three 4's -- with corresponding returns. The probability distribution for returns throwing a pair of these strange dice is

Return
Probability
Weighted expected return
$6
9/36 = 25%
1.500
$7
18/36 = 50%
3.500
$8
9/36 = 25%
2.000
Total
36/36 = 100%
$7.00

Again, the most likely return is $7 and the expected return is $7, but now the range is narrower -- from $6 to $8. This smaller variability affects risk. It is less likely you will have a miserable return. (Less variability also diminishes the possibility of a fabulous return.) For a person who is risk averse, it would be more desirable to throw the strange 3-4-only dice. There is less variability, and thus less risk, than with regular dice.

2.2.1 Probability Distribution

©2003 Professor Alan R. Palmiter

This page was last updated on: March 16, 2004