Ms B.

asked • 09/24/16

A card game using standard deck of 52 cards cost $1 to play If you draw a face card or an even number you lose.If you draw an ace you win 5$

help please

Ms B.

An if you draw an odd # you win 2$.What is the expected payoff? If the game is not fair,who had the advantage.? Explain your reasoning
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09/24/16

1 Expert Answer

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Neal D. answered • 09/24/16

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Expected outcome =
 
probability x value
 
= (4/52)$5 - (32/52)$1
 
= $5/13 - $8/13
 
= - $3/13
 
the expected outcome per game is negative which means you will lose more money than you will win
the game is not fair
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Neal D.

4/52($5) + 16/52($2) - 32/52($1)
 
I didn't have the odd numbers in my answer.  Work this out to get you expected outcome.
 
If you need help let me know.
 
 
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09/24/16

Ms B.

When I work the problem out to get the soloution do I add them together or?
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09/24/16

Neal D.

Yes, when you add them up you will get a number that represents your expected outcome for one game.  If that number is negative then you expect to lose that much per game you play.  It is only a fair game if the expected value is 0.   Now in order to get to that average, a person would have to play the game, maybe 100 or 500 times, add up their wins and losses, divide by the number of games played, and it would be close to the "Expected Value or Outcome".
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09/24/16

Ms B.

So how come you subtracted them at the top? cause I'm getting 51/43 adding them I'm so confused
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09/24/16

Neal D.

I am sorry,
 
For the ones that you will win $5 and $2, they will be positive values.   When you get an odd card you lose your $1, that is why you subtract (32/52)($1)
 
(4/52)$5 + (16/52)$2 - (32/52)$1 = 13/13 - 8/13 = 5/13 ; you expect to win just over 38 cents per game.  You want to play this game.
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09/24/16

Neal D.

When you get an odd you win $2 and an even or a face card you lose $1. An ace wins $5.
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09/24/16

Neal D.

Ms
 
You caught me when I was in a hurry to get to the dinner table.   Here is your final answer:
 
You expect to win on the average 38 cents per game, however, it costs you $1 to play.  Therefor, on the average, you will be losing 62 cents per game. 
 
This game is not FAIR!
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09/24/16

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