140k views
2 votes
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

User JayK
by
8.2k points

1 Answer

5 votes

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=(13)/(52)

The expected value of the game is,


E(X)=5((13)/(52))+2.50((13)/(52))-5((13)/(52))-2.50((13)/(52))=0

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

User Penelope
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories