A) To find the expected value of playing the game, we need to calculate the average amount of money Deshaun can expect to win or lose per draw.
The probability of drawing an even number is 5/10 (there are 5 even numbers out of 10 total numbers), and the amount Deshaun can win in this case is equal to the value of the card drawn.
The probability of drawing an odd number is also 5/10, and the amount Deshaun can lose in this case is $3.50.
So, the expected value (E) can be calculated as follows:
E = (probability of even) * (amount won) + (probability of odd) * (amount lost)
E = (5/10) * (average value of even numbers) + (5/10) * (-$3.50)
The average value of even numbers can be calculated as the sum of even numbers divided by the count of even numbers: (2+4+6+8+10)/5 = 6
E = (5/10) * 6 + (5/10) * (-$3.50)
E = $3 - $1.75
E = $1.25
Therefore, the expected value of playing the game is $1.25.
B) In the long run, after playing the game many times, Deshaun can expect to win an average of $1.25 per draw.
C) Deshaun can expect to gain money, specifically $1.25, per draw.