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Alexis is going to Vegas for the weekend! She decides to try her hand at a new game that Casino QuickCash is promoting. For this game, you pay $6 to play. A dealer shuffles and then randomly draws a card from a standard deck of 52 cards. If the card drawn is a diamond, Alexis wins nothing. If the card drawn is an even-numbered card (2,4,6,8, or 10) from the remaining three decks, Alexis wins $8. Otherwise, Alexis wins $12. a) Alexis's expected winnings per game is (rounded to the nearest cent):

Respuesta :

batolisis

Answer:

$10.46

Step-by-step explanation:

Amount that can be won by Alexis ( xi ) = $0, $8 , $12

probability ( pi )

P( $0 ) = 13 / 52 = 1 / 4

P( $8 ) = 15 / 39   ( given that she wins this when an even number is drawn from three remaining decks )

P ( $12 ) = 1 - 15/39 = 24 / 39

a) Alexis expected winnings per game

= ∑ xi * pi = ( 0 * 1/4 ) +  ( 8 * 15/39 ) + ( 12 * 24 / 39 )

                = $0 + ( 120 / 39 ) + ( 288 / 39 )  = $10.46

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