Please help with #32 Here is a transcription of the text seen in the image, designed for an educational website context:---### Probability and Expected Value Problems**27. Dice Roll Game**A pair of dice is rolled once. If a 7 appears, you lose $10, and if 11 or 12 appears, you win $11. What amount should you win or lose for any other number for the game to be fair?**28. Coin Toss Game**A coin is tossed three times. You lose $3 if 3 heads appear, lose $2 if 2 heads appear, and win $3 if 0 heads appear. What should be the result if 1 head appears for the game to be fair?**29. Card Draw Game - Kings**A card is drawn from a standard 52-card deck. Winning $10 occurs when a king is drawn, otherwise, you lose $1. What is the expected value of the game?**30. Card Draw Game - Diamonds**A card is drawn from a standard 52-card deck. You win $10 for a diamond, and lose $4 otherwise. What is the expected value of the game?**31. 5-Card Hand Game - Kings**A 5-card hand is dealt from a 52-card deck. If at least one king appears, you win $10; otherwise, you lose $1. What is the expected value of the game?**32. 5-Card Hand Game - Diamonds**A 5-card hand is dealt from a 52-card deck. Winning $10 occurs if at least one diamond is dealt; otherwise, you lose $4. What is the expected value of the game?**33. Payoff Table Analysis**Two courses of action, $ A_1 $ or $ A_2 $, are available. Which action provides the largest expected value? Calculate and determine it.### Additional Problems**37-41** - These sections discuss more probability games and raffle scenarios, engaging you in the analysis of random events.---This layout uses bullet points and sectioning to make comprehension and navigation more effective for learners.

Answered: Image /qna-images/answer/bd1a25b5-624a-4b26-93c0-7f9aeef6de22.jpgAnswer: Expected value of the game is 6.92 dollars.

Answered: A 5-card hand is dealt from a standard…

Math

Advanced Math

A 5-card hand is dealt from a standard 52-card deck. If the hand contains at least one diamond, you win $10; otherwise, you lose $4. What is the expected value of the game?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please help with #32

Here is a transcription of the text seen in the image, designed for an educational website context:

---

### Probability and Expected Value Problems

**27. Dice Roll Game**
A pair of dice is rolled once. If a 7 appears, you lose $10, and if 11 or 12 appears, you win $11. What amount should you win or lose for any other number for the game to be fair?

**28. Coin Toss Game**
A coin is tossed three times. You lose $3 if 3 heads appear, lose $2 if 2 heads appear, and win $3 if 0 heads appear. What should be the result if 1 head appears for the game to be fair?

**29. Card Draw Game - Kings**
A card is drawn from a standard 52-card deck. Winning $10 occurs when a king is drawn, otherwise, you lose $1. What is the expected value of the game?

**30. Card Draw Game - Diamonds**
A card is drawn from a standard 52-card deck. You win $10 for a diamond, and lose $4 otherwise. What is the expected value of the game?

**31. 5-Card Hand Game - Kings**
A 5-card hand is dealt from a 52-card deck. If at least one king appears, you win $10; otherwise, you lose $1. What is the expected value of the game?

**32. 5-Card Hand Game - Diamonds**
A 5-card hand is dealt from a 52-card deck. Winning $10 occurs if at least one diamond is dealt; otherwise, you lose $4. What is the expected value of the game?

**33. Payoff Table Analysis**
Two courses of action, $ A_1 $ or $ A_2 $, are available. Which action provides the largest expected value? Calculate and determine it.

### Additional Problems

**37-41** - These sections discuss more probability games and raffle scenarios, engaging you in the analysis of random events.

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