Question

6. Your favorite statistics instructor invites you to play a card game. He uses a standard deck of 52 cards. The deck itself is shuffled several times before the game starts. The game is simple: You draw one card (and then replace it randomly in the deck). If it is a face card, the instructor will give you $30. If not, you must pay him $2. a. How many face cards should we find in the deck? b. What is the expected (financial) value of this game? c. Should you accept the instructor’s invitation? (Yes or No?) d. Explain your answer to the question above using what you know about the expected value of this game. Again, please do your best to provide an explanation using everyday English.

Answer 1

a. There are 4 suits each containing 3 face cards, namely KIngs, Queens and jacks. So there are 12 face crads in totaal in a deck of 52 cards.

b. let X be the value I get/pay.

then X= 30 with probability 12/52

= -2 with probability 40/52

So,

= 5.38 ~5

So, if the game is played a number of times the expected amount I will get is $5 and thus same amount of expected loss for the instructor.

c. Yes.

d. As we see, there is a profit of $5 in the long run, I can definitely play the game with my instructor.But if there is a condition that the game will be played only for once/twice, and I dont have the fantasy of losing like $2, then I should not play the game.