Reattempt last question below, or select another question 2.36 Is it worth it?:

Question

Reattempt last question below, or select another 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, be wins S5, and he wins an extra $20 if he draws the ace of clubs. a) Andy's expected profit per game is: S 1.5577 b) Would you recommend this game to Andy as a good way to make money? Explain. e No, we expect Andy to lose money each time he plays this game Yes, Andy could be lucky and might earn money in the long-run playing this game License Points possible: 2 Unlimited attempts Score on last attempt: 1. Score in gradebook: 1 Submit

Explanation / Answer

a.) It is given that it costs Andy $2 to play the game.

He wins nothing for drawing cards 2 to 10, so we will forget about this.

Now he wins $3 for any face cards. In a deck of cards, out of 52 there are 12 face cards, 3 in each of the 4 suits.

So the probability of drawing any face card, say, P(Face cards) = 12/52

Now he wins $5 for drawing any ace, and there are 4 ace out of 52 cards.

So the probability of drawing an ace, say, P(any ace) = 4/52

And he wins extra $20 for drawing an ace of the suit club, and there is 1 ace of the suit club

So probability of drawing an ace of club, say, P(ace of club) = 1/52

So now he gains in total = $3*P(face cards) + $5*P(any ace) + $20*P(ace of a club)

Gain = $3 * 12/52 + $5 * 4/52 + $20 * 1/52

= 0.692 + 0.385 + 0.385

= 1.462

And it costs him $2 to play the game

So, his Expected Profit = $1.462 - $2

= -0.538

Since the expected profit is negative, Andy would lose the money each time he plays the game.

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.