Question

A person creates a game in which a person pays $5.00 to play. Then, they draw a single card from a standard

Answer 1

Answer:

Step-by-step explanation:

$5.00

Answer 2

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 = $\frac{12}{52}=\frac{3}{13}$

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  = $\frac{4}{52}=\frac{1}{13}$

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  = $\frac{36}{52}=\frac{9}{13}$

The expected money value playing this game is

E(x) = 5 × P(face cards) + 15 × P(Ace) - 5 × P(Other cards)

$E(x)=5\times \frac{3}{13}+15\times \frac{1}{13}-5\times \frac{9}{13}$

$E(x)=\frac{15}{13}+\frac{15}{13}-\frac{45}{13}$

$E(x)=-\frac{15}{13}$

$E(x)=-1.15384615385$

$E(x)\approx -1.15$

The expected money value playing this game is -$1.15

Therefore, the correct option is B.