In a gambling game a person draws a single card from an ordinary 52-card playing deck. A person is paid $18 for drawing a jack or a queen an

Question

In a gambling game a person draws a single card from an ordinary 52-card playing deck. A person is paid $18 for drawing a jack or a queen and $7 for drawing a king or an ace. A person who draws any other card pays $4. If a person plays this game, what is the expected gain?

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Rylee 1 week 2022-01-08T21:44:42+00:00 1 Answer 0 views 0

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    2022-01-08T21:45:50+00:00

    Answer:

    The expected gain is $1.077

    Step-by-step explanation:

    Consider the provided information.

    A person is paid $18 for drawing a jack or a queen.

    There are 4 jack and 4 queen in a deck of card.

    So probability of getting a jack or a queen is: \dfrac{8}{52}

    $7 for drawing a king or an ace.

    There are 4 king and 4 ace in a deck of card.

    So probability of getting a king or a ace is: \dfrac{8}{52}

    Now the remaining cards are: 52-8-8=36

    So probability of getting other card is:  \dfrac{36}{52}

    The expected probability is:

    E(Y)=\sum P(x_i)\times x_i

    E(Y)=18\times\dfrac{8}{52}+7\times\dfrac{8}{52}-4\times\dfrac{36}{52}

    E(Y)=\dfrac{36}{13}+\dfrac{14}{13}-\dfrac{36}{13}

    E(Y)=\dfrac{14}{13}\approx\$1.077

    Hence, the expected gain is $1.077

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45:7+7-4:2-5:5*4+35:2 =? ( )