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3. Weston is playing a game where on each turn, he flips two fair coins. If...
Stacy and George are playing the heads or tails game with a fair coin. The coin is flipped repeat...
Stacy and George are playing the heads or tails game with a fair coin. The coin is flipped repeatedly until either the fifth heads or the fifth tails appears. If the fifth heads occurs first, Stacy wins the game. Otherwise, George is the winner. Suppose that after the fifth flip, three heads and two tails have occurred. What is the probability that Stacy wins this game?
A player tosses two fair coins. He wins $5 if 2 heads occur, $2 it 1...
A player tosses two fair coins. He wins $5 if 2 heads occur, $2 it 1 head occurs and $1 if no heads occur. () Find his expected to play the game if it is to be fair? winnings. ) How much should he pay
Billy and Cam are playing the following game: each player has a coin and decides whether...
Billy and Cam are playing the following game: each player has a coin and decides whether to leave it as heads or tails before showdown (both player reveals their coin simultaneously). If both coins are heads, Billy wins $2. If both are tails, Billy wins $0.50. Otherwise, Cam wins $1. Find the optimal strategy for Billy.
Bob and Doug are playing the following game. Bob starts by rolling two fair dice; if...
Bob and Doug are playing the following game. Bob starts by rolling two fair dice; if the sum of his dice is six, then he wins the game. If not, then Doug rolls the dice, and if the sum of his rolls is seven, then he wins the game. If neither player wins the game during the first round, then they repeat the process (with Bob going first) until someone wins a round. What is the probability that Bob wins...
A subtraction game Subtraction games are two-player games in which there is a pile of objects,...
A subtraction game Subtraction games are two-player games in which there is a pile of objects, say coins. There are two players, Alice and Bob, who alternate turns subtracting 4.9. A SUBTRACTION GAME 19 from the pile some number of coins belonging to a set S (the subtraction set). Alice goes first. The first player who is unable to make a legal move loses. For example, suppose the initial pile contains 5 coins, and each player can, on his turn,...
Each game costs $5 and four COINS are flipped simultaneously. If you get one head you get $2, if you get two heads you g...
Each game costs $5 and four COINS are flipped simultaneously. If you get one head you get $2, if you get two heads you get $4, if you get three heads you get $10. Question： create the experimental probability distribution, expected value and bar graph. Compare the distribution, bar graph and expected value to the theoretical. Four Coin Filp ：1-100 Three COINS out of a hundred trials are heads with a probability of 25 Two COINS out of a hundred...
Question 2 13 marks Miss Piggy and Remy the Rat are playing a game of tennis,...
Question 2 13 marks Miss Piggy and Remy the Rat are playing a game of tennis, and they have just reached deuce! If a player wins the next point, that player has advantage. On the following point, she or he either wins the game or the game returns to deuce. Assume that for any point, Miss Piggy has probability 0.7 of winning the point, and so Remy the Rat has probabilit,y 0.3 of winning the point. Let S1,2,3,4,5 be the...
(6(4 pts) A player (Joe) goes to a casino and plays a fair game. The player...
(6(4 pts) A player (Joe) goes to a casino and plays a fair game. The player may wager any amount of money. There is a 0.5 probability of winning. If the player wins, then the player get twice the amount of the bet in winnings. If the player loses, the player gets nothing. Think of betting on a coin toss. If you win you double your money, if you lose you lose your money. This is a "fair" game because...
Problem 3. You play a game where you first choose a positive integer flip a fair...
Problem 3. You play a game where you first choose a positive integer flip a fair coinn times. You win a prize if you get exactly 2 heads. How should you choose n to maximize your chance of winning? What is the chance if winning with optimal choice of n? There are two equally good choices for the best n. Find both n and then an
I am playing a simplified version of the card game, "War," with my brother. We are...
I am playing a simplified version of the card game, "War," with my brother. We are playing with a subset of the deck, all of the numbered cards 2 through 10 (2:10). There are 4 cards of each number, resulting in 36 total cards in a single pile. First, I turn over a card. Next, he turns over a card. Whoever has the higher card wins and these "used" cards are discarded. If we turn over the same card, we...
A player tosses two fair coins. He wins $5 if 2 heads occur, $2 it 1 head occurs and $1 if no heads occur. () Find his expected to play the game if it is to be fair? winnings. ) How much should he pay
Question 2 13 marks Miss Piggy and Remy the Rat are playing a game of tennis, and they have just reached deuce! If a player wins the next point, that player has advantage. On the following point, she or he either wins the game or the game returns to deuce. Assume that for any point, Miss Piggy has probability 0.7 of winning the point, and so Remy the Rat has probabilit,y 0.3 of winning the point. Let S1,2,3,4,5 be the...
(6(4 pts) A player (Joe) goes to a casino and plays a fair game. The player may wager any amount of money. There is a 0.5 probability of winning. If the player wins, then the player get twice the amount of the bet in winnings. If the player loses, the player gets nothing. Think of betting on a coin toss. If you win you double your money, if you lose you lose your money. This is a "fair" game because...
Problem 3. You play a game where you first choose a positive integer flip a fair coinn times. You win a prize if you get exactly 2 heads. How should you choose n to maximize your chance of winning? What is the chance if winning with optimal choice of n? There are two equally good choices for the best n. Find both n and then an
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