SOLUTION: If you draw a card with a value of two or less from a standard deck of cards, I will pay you $317 . If not, you pay me $24 . (Aces are considered the highest card in the deck.)

Algebra ->  Probability-and-statistics -> SOLUTION: If you draw a card with a value of two or less from a standard deck of cards, I will pay you $317 . If not, you pay me $24 . (Aces are considered the highest card in the deck.)      Log On


   

Question 1203983: If you draw a card with a value of two or less from a standard deck of cards, I will pay you $317
. If not, you pay me $24
. (Aces are considered the highest card in the deck.)
Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The total number of cards in the deck: n=52
The number of cards which have a value of two or less: x=4

there are 4 possible cards you can draw to win the $317
The probability of this is then+4%2F52=1%2F13

On the flip side, there are 52-4=48 cards you could draw (the remaining cards in the deck), where you have to pay $24.
The probability of this is then 48%2F52=12%2F13

Thus, the expected value of this proposition is calculated by :
317%2A%281%2F13%29+%2B+%28-24%29%2A%2812%2F13%29+=29%2F13=2.23