Aboard 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.

The game is fair.

Step-by-step explanation:

We are given that a board game is played as follows; a number cube numbered 1 to 6 is rolled.

Total cases=6

If the number 1 comes up , then you get nothing

Number of favourable cases that you get nothing =1

The probability that you get nothing =

Using of probability formula : P(E)=

If number 2,3 or 5 comes up you win 40 points

Number of favourable cases that you wins=3

The probability that you wins =

Therefore, total number of points that you get =

If number 4 or 6 comes up then you lose 60 points

Number of favourable cases that you lose=2

The probability that you lose =

Therefore, total number of points that you get =

Therefore, the probability of winning is greater than the probability of lose or you get nothing and the point that you get is greater than the points you lose.

Hence , the game is fair.

step-by-step explanation:

the options are kind of confusing. i can tell you what i see going on here when i look at the graph.

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