Answer:
The expected value would be a gain of 1,5
Step-by-step explanation:
For any calculation of expecte value you should multiply the probability of every chance with his value or gain, for example, for this dice
If your roll 1
p(1) = 1/6, and his gain is -1
If your roll 2
p(2) = 1/6, and his gain is -2
If your roll 3
p(3) = 1/6, and his gain is -3
If your roll 4
p(4) = 1/6, and his gain is 4
If your roll 5
p(5) = 1/6, and his gain is 5
If your roll 6
p(6) = 1/6, and his gain is 6
So the expecte value would be
E = p(1)*(-1) + p(2)*(-2)+p(3)*(-3)+p(4)*(4)+p(5)*5+p(6)*6
p(1)=p(2)=p(3)=p(4)=p(5)=p(6)=1/6 because this dice is a cube, with even chances to fall in any face.
E = (1/6)*(-1-2-3+4+5+6)
E=(1/6)*(-6+15)
E=(1/6)*(9)
E=1,5
The expected value would be a gain of 1,5
