SOLUTION: Sam and Dana have bet money on a card game they are playing against each other. Sam pays $1 to play, and Dana pays $4. They will shuffle a deck of cards and flip over the top card.

Question 1162406: Sam and Dana have bet money on a card game they are playing against each other. Sam pays $1 to play, and Dana pays $4. They will shuffle a deck of cards and flip over the top card. If the top card is a heart, club, or diamond, Dana gets all $5. If the top card is a spade, then Sam gets all $5.
-What is the expected value of this game to Dana?
-If they play this game 10 times, what is the expected profit/loss for Sam?
-Is it beneficial for Sam to play this game? Justify your answer with a complete sentence.

Answer by Edwin McCravy(20064) (Show Source): You can put this solution on YOUR website!

Dana
            Winnings  Probability       Expectation
Non-spade     $1         0.75        ($1)(0.75) =  $0.75
Spade        -$4         0.25       (-$4)(0.25) = -$1.00
                              Total expectation = -$0.25

Dana's expected value is -$0.25 which means she will average losing 25 cents
per game.

--------------------------------------------------------

Sam
            Winnings  Probability       Expectation
Spade         $4         0.25        ($4)(0.25) =  $1.00
Non-spade    -$1         0.75       (-$1)(0.75) = -$0.75
                              Total expectation = +$0.25

Sam will average winning 25 cents per game.

--------------------------------------------------------  

Sam's expected profit is $0.25, which means he will average winning 25 cents
per game.

If they play 10 times, Sam's expected profit is 10×$.25 = $2.50.

It is beneficial for Sam to play since on the average, he will win 25 cents
per game. 
[Dana is stupid if she plays at all! J].

Edwin

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