Question

10) You are playing a game by drawing a card from a standard deck and replacing it. If the card is a face card, you win $20. If it is not a face card, you pay $5. There are 12 face cards in a deck of 52 cards.

What is the expected value of playing the game?

a. 0.77 b. 0.87 c.  1.77 d. 2.50

Answer 1

You are playing a game by drawing a card from a standard deck and replacing it.

number of face cards. =12

and number of non face cards = 52-12 = 40

The probability of face card is

P(face card) = Number of face cards/Total number of cards = 12/52

The probability of non face card is

P(non face card) = number of non face cards/Total number of cards = 40/52

The card is a face card, you win $20. If it is not a face card, you pay $5.

So Expected value E[x] of playing the game :

E[X] = 12/52 × 20 - 40/52 × 5 = 4.62- 3.85 = $ 0.77

Therefore the expected value of playing the game is $ 0.77

Answer - Option A