Question

3. You draw one card from a standard 52 card deck. If you draw a heart, you will win $10. If you draw a face card that is not a heart, you win $8. IF you pick any other card, you lose $6. What is the expected value of this game?

Answer 1

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.