Answer:
Expected value is not zero, game is not fair.
Step-by-step explanation:
chances to pick a face card of heart = 3/52
chances to pick a heart which is not a face card = 10/52
chances to pick any other card = 39/52
So,
Total earning = Profit loss on picking certain card * Probability of picking certain card
= 3/52 * 10 + 10/52 * 5 - 39/52 * 5 = $ (-115/52)
so the game is not fair as expected value is not zero.