Answer:
The expected value is -$0,63
Step-by-step explanation:
The expected value of a discrete variable x is given by:
E(x)=x1*p(x1)+x2*p(x2)+...+xn*p(xn)
Where x1, x2, .. xn are the posibles results that the variable x can take and p(x1), p(x2),...,P(xn) are their respective probabilities.
In this case, we have two possible results if we bet $12 on red. This results are:
1. The balls lands on red: in this case we keep the $12 we paid and we awarded 12. That means, we gain $12 and the probability of this case is the division of the number of red compartments by total number of compartments. So:
x1=$12
p(x1)=18/38
2. The balls doesn't land on red: in this case we lose the $12 that we bet and the probability is the division of number of compartments that aren't red by the total number of compartments. So:
x2=-$12
p(x2)=20/38
Then, replacing x1, x2, p(x1) and p(x2) on the equation of the expected value, we get:
E(x)=($12)*(18/38) + (-$12)*(20/38)
E(x)=$-0.63
So, the expected value if we bet $12 on red is to lose $0.63
