Question

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

Answer 1

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,

$P=\frac{13}{52}$

The expected value of the game is,

$E(X)=5(\frac{13}{52})+2.50(\frac{13}{52})-5(\frac{13}{52})-2.50(\frac{13}{52})=0$

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