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 this game? Is he more or less likely than Doug to win?
Homework Answers
P (Probability that bob wins ) = is given below
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Bob and Doug are playing the following game. Bob starts by
rolling two fair dice; if...
2. "Craps" is a game played by rolling two fair dice. To play one round of...
2. "Craps" is a game played by rolling two fair dice. To play one round of this game, the player rolls the dice and the outcome is determined by the following rules: If the total number of dots is 7 or 11 (a "natural"), then the player wins. If the total number of dots is 2, 3, or 12 C'craps"), then the player loses. If the total number of dots is 4, 5, 6,8,9, or 10, then this number is...
Bob plays a game in which he rolls a pair of fair 6-sided dice once. He...
Bob plays a game in which he rolls a pair of fair 6-sided dice once. He adds the number of dots on both dice to create a sum. He loses $1 if he rolls a sum less than 5 doesn’t win or lose anything if he rolls a sum that is higher than 4, but less than 8 wins $1 if he rolls a sum that’s higher than 7 but less than 12 wins $2 if he rolls a sum...
4. Alice and Bob take turns rolling a fair six sided die. They keep playing this...
4. Alice and Bob take turns rolling a fair six sided die. They keep playing this game until someone gets a 6, and that person is declared the winner. Alice goes first. Find the probability that Alice wins the game. Hint: The probability should be more than 0.5 Example of Alice winning in 5 turns: В А В А 2 2 6
Example Consider the following dice game. A pair of standard ( fair ) dice are repeatedly...
Example Consider the following dice game. A pair of standard ( fair ) dice are repeatedly rolled. If a ’ 7 ’ comes up before an ’ 11 ’ , then the player wins, otherwise the player loses. Let W be the event that the player wins. Find P(W). To say the dice are fair is equivalent to assuming that Laplace’s rule holds and the 36 possible outcomes for a throw of the dice are equally likely. For convenience, an...
Question 3 [10 points] Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 90% of their games. To make up for this, if Doug wins a game he will spot Bob tive points in th...
Question 3 [10 points] Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 90% of their games. To make up for this, if Doug wins a game he will spot Bob tive points in their next game. if Doug wins again he will spot Bob ten points the next game, and if he still wins the next game he will spot him ifteen points, and continue to spot hinm ifteen points as...
2. A game of chance costs $5 to play and consists of rolling a five fair...
2. A game of chance costs $5 to play and consists of rolling a five fair dice. If at least four of the dice shows a number (strictly) greater than 2 then the player wins $10. (a) What is the expected net winnings from one game? (b) Suppose that a gambler plans to keep playing this game until he has lost a total of four games, what is his expected net loss or net winnings under this strategy?
Two player Dice game In C++ The game of ancient game of horse, not the basketball...
Two player Dice game In C++ The game of ancient game of horse, not the basketball version, is a two player game in which the first player to reach a score of 100 wins. Players take alternating turns. On each player’s turn he/she rolls a six-sided dice. After each roll: a. If the player rolls a 3-6 then he/she can either Roll again or Hold. If the player holds then the player gets all of the points summed up during...
Question 9 [10 points] Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, an...
Question 9 [10 points] Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 90% of their games. To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will spot Bob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points as...
1 point) Three brothers play a game with a pair of fair (six-sided) dice. Scott will...
1 point) Three brothers play a game with a pair of fair (six-sided) dice. Scott will win if the sum of the dice is 3, Dave will win if 9, and Jim if 11 They will roll the die until a winner is declared Part (c) Realizing this, theoretically, is a game that could go on forever..the three brothers decide that if no winner has been decided in three rolls or "turns" Scott will be deemed the winner. Let Y...
Question 9 [10 points] Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, an...
Question 9 [10 points] Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 70% of their games To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will spot Bob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points as...
2. "Craps" is a game played by rolling two fair dice. To play one round of this game, the player rolls the dice and the outcome is determined by the following rules: If the total number of dots is 7 or 11 (a "natural"), then the player wins. If the total number of dots is 2, 3, or 12 C'craps"), then the player loses. If the total number of dots is 4, 5, 6,8,9, or 10, then this number is...
4. Alice and Bob take turns rolling a fair six sided die. They keep playing this game until someone gets a 6, and that person is declared the winner. Alice goes first. Find the probability that Alice wins the game. Hint: The probability should be more than 0.5 Example of Alice winning in 5 turns: В А В А 2 2 6
Question 3 [10 points] Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 90% of their games. To make up for this, if Doug wins a game he will spot Bob tive points in their next game. if Doug wins again he will spot Bob ten points the next game, and if he still wins the next game he will spot him ifteen points, and continue to spot hinm ifteen points as...
2. A game of chance costs $5 to play and consists of rolling a five fair dice. If at least four of the dice shows a number (strictly) greater than 2 then the player wins $10. (a) What is the expected net winnings from one game? (b) Suppose that a gambler plans to keep playing this game until he has lost a total of four games, what is his expected net loss or net winnings under this strategy?
Question 9 [10 points] Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 90% of their games. To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will spot Bob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points as...
1 point) Three brothers play a game with a pair of fair (six-sided) dice. Scott will win if the sum of the dice is 3, Dave will win if 9, and Jim if 11 They will roll the die until a winner is declared Part (c) Realizing this, theoretically, is a game that could go on forever..the three brothers decide that if no winner has been decided in three rolls or "turns" Scott will be deemed the winner. Let Y...
Question 9 [10 points] Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 70% of their games To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will spot Bob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points as...
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