A board game is played as follows: a number cube numbered 1 to 6 is rolled. If the number 1 comes up, you get nothing. If the number 2, 3, or 5 comes up, you win 40 points. If the number 4 or 6 comes up, you lose 60 points. Use the expected value to prove whether or not the game is fair. Show all work for full credit. Three or more sentences, please!!!

This is a fair game.

To find the expected value, we need to first multiply the fraction for each event by the outcome. Then, add all of the values together.

(1/6) x 0 = (1/2) x 40 + (1/3) x (-60)

0 + 20 + (-20) = 0

Since, the outcome is neither positive or negative, it is a fair game.

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batolisis batolisis · Answer 2 · 2022-05-13T12:08:13+02:00

The game is fair, using the expected value to solve for the probability of wining or losing.

Meaning of probability and full working

Probability is the degree of occurrence of an event. it can also be said to be the chance for an event to occur.

The full working is shown below:

Probability of wining = probability of losing or gaining nothing

In a game you either lose or win that's what helps us to check if it is fair or not

probability of winning = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

probability of losing = [tex]\frac{2}{6}[/tex]

probability of gaining nothing = [tex]\frac{1}{6}[/tex]

[tex]\frac{1}{2}[/tex] = [tex]\frac{2}{6}[/tex] + [tex]\frac{1}{6}[/tex]

[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] (the chances are equal)

In conclusion, The game is fair, using the expected value.

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