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A game is played with a standard deck of cards using the following rules: A player has to draw a card from the deck of cards. He/she wins $5 if he/she draws a club card, and $2.50 if he/she draws a spade. If the player draws a diamond, he/she loses $5, and $2.50 if he/she draws a heart. There is no entry fee for the game. Is the game fair?NoYesCan’t be determined

Respuesta :

Given:

The player draws a club card, then wins $5 and $2.50 if he draws a spade.

If the player draws a diamond, he loses $5 and $2.50 if he draws a heart.

The probability of drawing each club card, spade, diamond, and heart is given as,

[tex]P=\frac{13}{52}[/tex]

The expected value of the game is,

[tex]E(X)=5(\frac{13}{52})+2.50(\frac{13}{52})-5(\frac{13}{52})-2.50(\frac{13}{52})=0[/tex]

As the expected value is zero. So, the game is fair.

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