Respuesta :
Answer:
Option B.
Step-by-step explanation:
Cost of game = $5.00
If they draw a face card, they win $10.00 (i.e. they get their $5.00 back and get an extra $5.00).
Winning amount = $5
Number of face cards = 12
Probability of getting a face card = [tex]\frac{12}{52}=\frac{3}{13}[/tex]
If they draw an ace, they win $20.00 (i.e. they get their $5.00 back and get an extra $15.00).
Winning amount = $15
Number of ace = 4
Probability of getting an ace = [tex]\frac{4}{52}=\frac{1}{13}[/tex]
Any other draw they lose their money.
Number of other card (Exclude ace and face cards) = 52-4-12=36
Probability of getting other cards = [tex]\frac{36}{52}=\frac{9}{13}[/tex]
The expected money value playing this game is
E(x) = 5 × P(face cards) + 15 × P(Ace) - 5 × P(Other cards)
[tex]E(x)=5\times \frac{3}{13}+15\times \frac{1}{13}-5\times \frac{9}{13}[/tex]
[tex]E(x)=\frac{15}{13}+\frac{15}{13}-\frac{45}{13}[/tex]
[tex]E(x)=-\frac{15}{13}[/tex]
[tex]E(x)=-1.15384615385[/tex]
[tex]E(x)\approx -1.15[/tex]
The expected money value playing this game is -$1.15
Therefore, the correct option is B.
