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6 October, 15:43

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.

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  1. 6 October, 19:34
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    Option B.

    Step-by-step 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.
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