Answer:
The expected value is defined as:
EV = ∑xₙ*pₙ
Where xₙ represents the n-th event, and pₙ is the probability of that event.
Now, the events are:
The possible outcomes are: {2, 3, 4, 5, 6, 7, 8, 9, 10} 9 in total.
Winning $1, when the number is odd. The outcomes in this case are: {3. 5. 7. 9}
4 out of 9, then the probability is p = 4/9.
Lossing $1 when the number is even. The outcomes in this case are {2, 4, 6, 8, 10}
5 out of 9, the probability is p = 5/9.
Then the expected value is:
EV = (4/9)*$1 - (5/9)*$1 = (-1/9)*$1 = -$0.11...
