Question

2.36 Is it worth it?: 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 $25 if he draws the ace of clubs. Round answers to 2 decimal places. a) Andy's expected profit per game is: $ b) Would you recommend this game to Andy as a good way to make money? Explain. Yes, Andy could be lucky and might earn money in the long-run playing this game No, we expect Andy to lose money each time he plays this game

Answer 1

Answer:

a) - 0.54

b) No, we expect Andy to lose money each time he plays this game. This game is not a good way to make money.

Step-by-step explanation:

We are told the game costs $2 to play.

In a card game, we have the following:

Total number of cards = 52

Number of number cards (2-10)=36

Number of face cards = 12

Number of ace = 3

Number of ace of clubs = 1

The probability and profits of the game is calculated below.

Probability he gets a number card 2-10 =$\frac{36}{52} = 0.69$

Profit = - $2

Probability he gets a face card:

$\frac{12}{52} = 0.23$

Profit = $3 - $2 = $1

Probability he gets an ace:

$\frac{3}{52} = 0.06$

Profit = $5 - $2 =$3

Probability he gets an ace of clubs:

$\frac{1}{52} = 0.02$

Profit = $25 - $2 =$23

Andy's expected profit per game wil be given as:

E = probability * profit

= [(0.69 * -2)+(0.23 * 1)+(0.06 * 3)+(0.02 * 23)]

= -0.54

b) No, we expect Andy to lose money each time he plays this game. This game is not a good way to make money.

Andy's expected profit per game (-0.542) is negative, which means he doesn't make any profit per game.