Question

Two students created a game of dice. They determined that each roll would add the value of the die if it was an odd numberIf the roll was even, it would subtract the value of the die. (For example, a roll of 2 would subtract two points, but a roll of 3 would add three points.) What is the expected value for this game?

Answer 1

its definitely  -0.5

Answer 2

Answer:

The expected value for this game is:

                          -0.5

Step-by-step explanation:

We know that expectation of the game is the sum of the product of the probability and the score of each of the game.

We know that on rolling a die the outcomes are: {1,2,3,4,5,6}

This means that the probability of rolling each of the number is:

               1/6

When odd comes up the score is added.

i.e. if 1 comes then +1 is added to the score.

if 3 comes up then +3 is added to the score.

if 5 comes up then +5 is added to the score.

Also, if even is rolled then the score is subtracted.

i.e. if 2 comes up then -2 is subtracted from the score.

if 4 comes up then -4 is subtracted from the score.

if 6 comes up then -6 is subtracted from the score.

Hence, the expected score is calculated as follows:

$=\dfrac{1}{6}\times 1+\dfrac{1}{6}\times (-2)+\dfrac{1}{6}\times 3+\dfrac{1}{6}\times (-4)+\dfrac{1}{6}\times 5+\dfrac{1}{6}\times (-6)\\\\\\=\dfrac{1}{6}\times (1-2+3-4+5-6)\\\\\\=\dfrac{-3}{6}\\\\\\=-\dfrac{1}{2}\\\\\\=-0.5$

                  Hence, the answer is:

                      -0.5