Answer:
The expected value to lose is $0.32
Step-by-step explanation:
First you find the average value from the winnings.
You do this by multiplying the probablity of victory by how much you would win: 1/38 * 210 == $5.526
Then you add that to the average value of losing times the probablity of losing: 37/38 * -6 == $ -5.842 (it is important to have the negative there because you are losing money)
Then you add those together and you get your anwser:
$5.526 - $5.842 = $0.316 which rounds up to -$0.32
The expected value to lose is $0.32