Respuesta :
Answer and Explanation:
Given : You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $5. For any club, you get $10 plus an extra $50 for the ace of clubs.
To find :
a) Create a probability model for the amount you win at this game.
b) Find the expected amount you'll win.
c) How much would you be willing to pay to play this game?
Solution :
In a deck of 52 cards,
Red cards = 26 and Black card = 26
Heart = 13, Diamond=13 and Spade = 13, Club =13
If you get a red card, you win nothing.
i.e. At X=0, [tex]P(X)=\frac{26}{52}=0.5[/tex]
If you get a spade, you win $5.
i.e. At X=5, [tex]P(X)=\frac{13}{52}=0.25[/tex]
If you get a club, you get $10.
i.e. At X=10, [tex]P(X)=\frac{13}{52}=0.25[/tex]
If you get a ace of clubs, you get $50.
i.e. At X=50, [tex]P(X)=\frac{1}{52}=0.2[/tex]
a) A probability model for the amount you win at this game.
X | 0 5 10 50
P(X) | 0.5 0.25 0.25 0.2
b) The expected amount you'll win.
[tex]E(X)=\sum XP(X)[/tex]
[tex]E(X)=0(0.5)+5(0.25)+10(0.25)+50(0.2)[/tex]
[tex]E(X)=0+1.25+2.5+10[/tex]
[tex]E(X)=13.75[/tex]
c) How much would you be willing to pay to play this game.
An amount which is less or equal to the expected value.
