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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?

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
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
= lil B 27. A pair of dice is rolled once. Suppose you lose $10 if a 7 turns up and win $11 if an 11 or 12 turns up. How much should you win or lose if any other number turns up in order for the game to be fair? 28. A coin is tossed three times. Suppose you lose $3 if 3 heads appear, lose $2 if 2 heads appear, and win $3 if 0 heads ap- pear. How much should you win or lose if 1 head appears in order for the game to be fair? 29. A card is drawn from a standard 52-card deck. If the card is a king, you win $10; otherwise, you lose $1. What is the expected value of the game? 30. A card is drawn from a standard 52-card deck. If the card is a diamond, you win $10; otherwise, you lose $4. What is the expected value of the game? 31. A 5-card hand is dealt from a standard 52-card deck. If the hand contains at least one king, you win $10; otherwise, you lose $1. What is the expected value of the game? 32. 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? 33. The payoff table for two courses of action, A₁ or A2, is given below. Which of the two actions will produce the largest expected value? What is it? 1 NOV 11 37. A gam- to play $100 b winnin would 38. A gam to play bet) fa Would influe C 39. Five t Ticket ed as $20, a raffle 40. Ten th librar $1,00 expec 41. A box samp assoc (A) I (B) I
Transcribed Image Text:= lil B 27. A pair of dice is rolled once. Suppose you lose $10 if a 7 turns up and win $11 if an 11 or 12 turns up. How much should you win or lose if any other number turns up in order for the game to be fair? 28. A coin is tossed three times. Suppose you lose $3 if 3 heads appear, lose $2 if 2 heads appear, and win $3 if 0 heads ap- pear. How much should you win or lose if 1 head appears in order for the game to be fair? 29. A card is drawn from a standard 52-card deck. If the card is a king, you win $10; otherwise, you lose $1. What is the expected value of the game? 30. A card is drawn from a standard 52-card deck. If the card is a diamond, you win $10; otherwise, you lose $4. What is the expected value of the game? 31. A 5-card hand is dealt from a standard 52-card deck. If the hand contains at least one king, you win $10; otherwise, you lose $1. What is the expected value of the game? 32. 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? 33. The payoff table for two courses of action, A₁ or A2, is given below. Which of the two actions will produce the largest expected value? What is it? 1 NOV 11 37. A gam- to play $100 b winnin would 38. A gam to play bet) fa Would influe C 39. Five t Ticket ed as $20, a raffle 40. Ten th librar $1,00 expec 41. A box samp assoc (A) I (B) I
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