math: expected value/profit?

I am having trouble figuring out the answer.

Q: Andy is gambling. 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. What is Andy's expected profit per game?

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  • Mike G
    Lv 7
    3 years ago
    Favorite Answer

    E(X) = -2+3*(12/52)+5*(3/52)+25*(1/52)

    = -2+[36+15+25]/52

    = -26/13+19/13

    = -7/13

    = -$0.54

    He will lose on average 54 cents per game

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  • 3 years ago

    His expected winnings per game are

    .. 12/52*$3 +4/52*$5 +1/52*$20 = $76/53 ≈ $1.46

    After subtracting his cost, Andy can expect to lose $0.54 per game.

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