Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card (jack, queen or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs. Report to two decimal places (e. g., X. xx - do not enter a $ sign). Find Andy's expected profit per game.

0.51

Explanation:

Given the following :

Cost of playing = $2

Total cards in a deck = 52

Number card(2 - 10) = (4 * 9) = 36

P(number card) = 36 /52 = 9 / 13 = 0.69

Winning for number card = $0 - $2 = - $2

Face card = (3 * 4) = 12

P(face card) = 12 / 52 = 3 / 13 = 0.23

Winning on face card = $3 - $2 = $1

Ace excluding ace of club= 3

P(ace) = 3 / 52 = 1 / 13 = 0.057 = 0.06

Winning on ace = $5 - $2 = $3

Ace of club = 1

P(ace of club) = 1/52 = 0.019 = 0.02

Winning ( additional) = $20

Total winning = $20 + $5 - $2 = $23

Expected profit per game :

Σ(Probability * winning)

Σ(-2 * 0.69) + (1 * 0.23) * (0.06 * 3) + (0.02 * 23)

Σ (-1.38 + 0.23 + 0.18 + 0.46)

= 0.51