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.

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: