Question

If you draw a card with a value of four or less from a standard deck of cards, I will pay you $173.  If not, you pay me $⁢48.  (Aces are considered the highest card in the deck.)

Step 2 of 2 :  

If you played this game 685 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be entered as negative.

Answer 1

We will first find the probabilities of occurrances of the above mentioned events.

Let A denote the event of drawing a card with a value of four or less from a standard deck of cards Since there are 4 designs with three cards each satisfying the above criteria

Then

Now expected value of this game when played once =

Hence $3 is the expected value for playing the game once

Now playing this game 685 times are independent of each other. Expected value of playing this game 685 times =685*$3=$2055. This is the amount that is expected to win if the game is played 685 times