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DISCRETE MATH
Suppose a person offers to play a game with you. You pay $1 to...
Suppose you make a dollar bet on a game in which there is a 1 in 5 chance to win
Suppose you make a dollar bet on a game in which there is a 1 in 5 chance to win. If you win, you win two dollars. On average, you will lose playing this game and each play costs you _______ cents. If you play 200 times, you can expect to lose around _______ dollar .You play roulette betting one dollar on the number 5 each time. The bet pays 35 to 1. You have a 1 in 38 chance to...
In playing a game, you win or lose 1 dollar with probability 0.5. If you play the game independen...
Use Central Limit Theorem Please!
In playing a game, you win or lose 1 dollar with probability 0.5. If you play the game independently 1,000 times, what is (approximately) the probability that your fortune (the total amount you won or lost) is at least 10 dollars? (Use the Central Limit Theorem)
In playing a game, you win or lose 1 dollar with probability 0.5. If you play the game independently 1,000 times, what is (approximately) the probability that your fortune...
15. Your friend challenges you to a game. She says that she is going to roll...
15. Your friend challenges you to a game. She says that she is going to roll 2 6-sided dice. If the first die rolls at least 5, you win if the second die rolls less than 5. If the first die rolls less than 5, you win if the second die rolls at least 5. This seems fair. Is it? (a) What is the probability that you win this game? To incentivize you, your friend says that she will pay...
Suppose you can place a bet in the following game. You flip a fair coin (50-50...
Suppose you can place a bet in the following game. You flip a fair coin (50-50 chance it lands heads). If it lands heads, you get 4 dollars, if it lands tails, you pay 1 dollar. This is the only bet you can make. If you don't make the bet you will neither gain nor lose money. Should you place the bet?
Suppose you can place a bet in the following game. You flip a fair coin (50-50...
Suppose you can place a bet in the following game. You flip a fair coin (50-50 chance it lands heads). If it lands heads, you get 4 dollars, if it lands tails, you pay 1 dollar. This is the only bet you can make. If you don't make the bet you will neither gain nor lose money. What is the utility for you of the coin landing tails if you make the bet (assume utility is dollars)?
A street hustler offers you the following game: Each play you roll 2 dice. Each play...
A street hustler offers you the following game: Each play you roll 2 dice. Each play costs $1 If you roll an even number you win that amount If you roll an odd number you lose that amount in addition to the $1. 1) Calculate the probabilities P(X 1+X 2-3) 2) write the reward function, rie), where s -X + X, in the following form r(e)-a 3) What is the expected reward? Should you take up the bet?
In a dice game, you roll a fair die three times, independently. If you don’t roll...
In a dice game, you roll a fair die three times, independently. If you don’t roll any sixes, you lose 1 dollar. If you roll a six exactly once, you win one dollar. If you roll a six exactly twice, you win two dollars. If you roll a six all three times, you win k dollars. (A) Let k = 3. What is the expected value of the amount you would win by playing this game (rounded to the nearest...
(1) Suppose you are to play a version of poker where you are dealt five cards...
(1) Suppose you are to play a version of poker where you are dealt five cards and win only if you are dealt a three of kind. That is, you win only when your five card hand contains a triple of the same rank, and two other cards each of different ranks than each other and different than the triple (examples: AAA94, 55579). If you win, you will win S100. If you lose, you have to pay some amount of...
Suppose that a fair coin is tossed ten times. Each time it lands heads you win...
Suppose that a fair coin is tossed ten times. Each time it lands heads you win a dollar, and each time it lands tails you lose a dollar. Calculate the probability that your total winnings at the end of this game total two dollars, and the probability that your total winnings total negative two dollars.
Suppose you have a six sided die. One face is printed with the number 1. Two faces...
Suppose you have a six sided die. One face is printed with the number 1. Two faces are printed with the number 2. Three faces are printed with the number 3. You also have 3 coins: C_1, C_2, and C_3. C_1 will land Heads with probability 1/5. C_2 will land Heads with probability 1/3. C_3 will land Heads with probability 1/2. You roll the die. If the die lands with a 1 face up, flip coin C_1 If the die lands with...
Use Central Limit Theorem Please!
In playing a game, you win or lose 1 dollar with probability 0.5. If you play the game independently 1,000 times, what is (approximately) the probability that your fortune (the total amount you won or lost) is at least 10 dollars? (Use the Central Limit Theorem)
In playing a game, you win or lose 1 dollar with probability 0.5. If you play the game independently 1,000 times, what is (approximately) the probability that your fortune...
15. Your friend challenges you to a game. She says that she is going to roll 2 6-sided dice. If the first die rolls at least 5, you win if the second die rolls less than 5. If the first die rolls less than 5, you win if the second die rolls at least 5. This seems fair. Is it? (a) What is the probability that you win this game? To incentivize you, your friend says that she will pay...
A street hustler offers you the following game: Each play you roll 2 dice. Each play costs $1 If you roll an even number you win that amount If you roll an odd number you lose that amount in addition to the $1. 1) Calculate the probabilities P(X 1+X 2-3) 2) write the reward function, rie), where s -X + X, in the following form r(e)-a 3) What is the expected reward? Should you take up the bet?
(1) Suppose you are to play a version of poker where you are dealt five cards and win only if you are dealt a three of kind. That is, you win only when your five card hand contains a triple of the same rank, and two other cards each of different ranks than each other and different than the triple (examples: AAA94, 55579). If you win, you will win S100. If you lose, you have to pay some amount of...
Suppose that a fair coin is tossed ten times. Each time it lands heads you win a dollar, and each time it lands tails you lose a dollar. Calculate the probability that your total winnings at the end of this game total two dollars, and the probability that your total winnings total negative two dollars.
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