If you draw a card with a value of five or less from a standard deck of cards, I will pay you $7$ 7. If not, you pay me $7$ 7. (Aces are con

Question

If you draw a card with a value of five or less from a standard deck of cards, I will pay you $7$ 7. If not, you pay me $7$ 7. (Aces are considered the highest card in the deck.) Step 2 of 2 : If you played this game 543543 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.

in progress 0
MichaelMet 6 months 2021-07-24T02:40:03+00:00 1 Answers 13 views 0

Answers ( )

    0
    2021-07-24T02:41:21+00:00

    Answer:

    Amount = -\$1461.9

    Step-by-step explanation:

    We have the following:

    Total = 52 — cards in a standard deck

    Represent cards with a value of 5 or less with x

    So:  x = \{2, 3, 4, 5\} i.e 4 cards

    However, each of these has a frequency of 4.

    So: n(x) = 4\ cards* 4

    n(x) = 16

    The probability is:

    p(x) = \frac{16}{52}

    The cost of this is:

    C(x) = +\$7

    Represent cards with a value of above 5 with y

    n(y) = 52 - 16

    n(y) = 36

    The probability is:

    p(y) = \frac{36}{52}

    The cost of this is:

    C(y) = -\$7 — It is negative because you lost

    In a game, your expected amount is:

    E = n(x) * C(x) + n(y) * C(y)

    E = \frac{16}{52} * (+\$7) + \frac{36}{52} * (-\$7)

    E = \frac{16* \$7}{52}  - \frac{36* \$7}{52}

    E = \frac{\$112}{52}  - \frac{\$252}{52}

    E = \frac{\$112 - \$252}{52}

    E = -\frac{\$140}{52}

    When you play 543 times, the expected amount is:

    Amount = E * 543

    Amount = -\frac{\$140}{52} *543

    Amount = -\frac{\$140 *543}{52}

    Amount = -\frac{\$76020}{52}

    Amount = -\$1461.9

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )