If you draw a card with a value of four or less from a standard deck of cards, I will pay you $59. If not, you pay me $14.

Question

If you draw a card with a value of four or less from a standard deck of cards, I will pay you $59$⁢59. If not, you pay me $14$⁢14. (Aces are considered the highest card in the deck.)

Answer 1

There is no question here, but this is not a good deal for you, the person paying out.

 

The probability that you get 4 or less is 4/13 and you lose.

The probability that you get higher than a 4 is 9/13 and you win.

 

let's say that each card came out once in 13 picks.....4 should be 4 or less while 9 should be greater than 4. That means you would pay out 59*4=$236 and you would collect 14*9= $126. So you come out losing money.

 

Maybe you did this with expected value?

 

your expected value is (4/13)(-59) + (9/13)(14)=-18.15+9.69=-8.46. This means that you would expect to lose $8.46, on average, every time you played this game. Not good for you.

 

Hope this helped.