Two players take turns tossing a fair, six-sided die. The first player to roll a 6 wins the game. Determine the probability that the player who wins will be the one who tossed first.
Two players take turns tossing a fair, six-sided die. The first player to roll a 6...
Players A and B each roll a fair 6-sided die. The player with the higher score wins ¤1 from the other player. If both players have equal scores, the game is a draw and no one wins anything. i. Let X denote the winnings of player A from one round of this game. State the probability mass function of X. Calculate the expectation E(X) and variance Var(X). ii. What is the conditional probability that player A rolls , given that...
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
The game of Pig is a simple two-player dice game in which the first player to reach 100 or more points wins. Players take turns. On each turn, a player rolls a six-sided die: If the player rolls a 1, then the player gets no new points and it becomes the other player’s turn. If the player rolls 2 through 6, then he or she can either ROLL AGAIN or HOLD: At this point, the sum of all rolls...
John and Paul play the following game. They each roll one fair 6-sided die. John wins the game if his score is larger than Paul’s score or if the product of the scores is an odd number. Find the probability that John wins.
A) Suppose I roll two fair six-sided dice. What is the probability that I rolled a total of 5? B) Suppose I roll two fair six-sided die and I announce that the sum of the two die is 6 or less. What is the probability that I rolled a total of 5?
in a game, you toss a fair coin and a fair six sided die. if you toss a heads on the coin and roll either a 3 or a 6 on the die, you win $30. otherwise, you lose $6. what is the expected profit of one round of this game
Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. What is the probability that both die roll ones? What is the probability that exactly one die rolls a one? What is the probability that neither die rolls a one? What is the expected number of ones? If you did this 1000 times, approximately how many times would you expect that exactly one die would roll...
A player pays $10 to roll two six-sided dice. She wins $50 if she rolls a sum of 10 and $20 if she rolls a sum of 8. Given the probability distribution for the game (below), compute the expected value of the game to the nearest cent.
In a game, a single event consists of fair six-sided die begin thrown followed by flip of a fair two-sided coin. a. state the number of possible outcome in the sample space b. find the probability that a single randomly-selected turn will be include the coin toss coming up "heads" c.find the probability that a single randomly - selected turn in include a "6" coming up on the die d.find the probability that a single randomly-selected turn will include a...
Suppose a casino has a game where a fair six-sided die is rolled. If an odd number is rolled, the player loses $2. If a six is rolled, the player wins $20. Otherwise, the player loses $1. If a player played this game 1000 times, how much money should he expect to gain (or lose)? Show work.