If you draw a card with a value of four or less from a standard deck of cards, i will pay you $37$⁢37. if not, you pay me $15$⁢15. (aces are considered the highest card in the deck.) step 2 of 2 : if you played this game 713713 times how much would you expect to win or lose? round your answer to two decimal places. losses must be entered as negative.

We have that in a deck of cards, there are 3 kinds of cards that have value under 4 (or equal). These are 2,3,4 and they are in total 4*3=12. The probability that we draw such a card is 12/52=0.23. Hence the probability that we do not draw such a card is 1-0.23=0.77. If we play the game once, we will get 0.23 of the times 37$ and 0.77 of the times 15$. Hence, the net total expected outcome is: 0.23*37$-0.77*15$=-3.001$. After playing this game for 713 times, we will lose in total: 713*3.001$=2139.74$. The losses will be -2139.74$