Answer:
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
