Question

Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card ( jack, queen or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs.

Create a probability model and find Andy's expected profit per game.

Answer 1

Option B.

Explanation:

Cost of game = $5.00

If they draw a face card, they win $10.00 (i.e. they get their $5.00 back and get an extra $5.00).

Winning amount = $5

Number of face cards = 12

Probability of getting a face card =

If they draw an ace, they win $20.00 (i.e. they get their $5.00 back and get an extra $15.00).

Winning amount = $15

Number of ace = 4

Probability of getting an ace =

Any other draw they lose their money.

Number of other card (Exclude ace and face cards) = 52-4-12=36

Probability of getting other cards =

The expected money value playing this game is

E(x) = 5 × P(face cards) + 15 × P(Ace) - 5 × P(Other cards)

The expected money value playing this game is -$1.15

Therefore, the correct option is B.