Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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Transcribed Image Text: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.
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