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

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

Answer 2

Based on the calculations, the expected value for this game of dice is equal to

$\frac{-1}{2}$ or -0.5.

What is an expected value?

An expected value can be defined as the product of each value in a data set and the sum of their probability.

How to determine the expected value.

For a game of dice, the total number of outcomes (expected values) is equal to six (6). Thus, the probability of rolling each number is $\frac{1}{6}$.

For the odd numbers:

If 1 comes up, then one (1) point would be added to the score.

If 3 comes up, then three (3) points would be added to the score.

If 5 comes up, then five (5) point would be added to the score.

For the even numbers:

If 2 comes up, then two (2) point would be subtracted to the score.

If 4 comes up, then four (4) points would be subtracted to the score.

If 6 comes up, then six (6) point would be subtracted to the score.

Based on the above information, the expected value is given by:

$Value =[ \frac{1}{6} \times 1]+\frac{1}{6} \times (-2)+[\frac{1}{6} \times 3]+\frac{1}{6} \times (-4)+\frac{1}{6} \times (5)+\frac{1}{6} \times( -6)\\\\Value =\frac{1}{6} \times (1-2+3-4+5-6)\\\\Value =\frac{1}{6} \times( -3)\\\\Value =\frac{-3}{6} \\\\Value =\frac{-1}{2}$

Read more on probability here: https://brainly.com/question/25870256