1). Two dice are rolled, and the results are added. Assuming that this number is greater...
1). Two dice are rolled, and the results are added. Assuming that this number is greater than or equal to 8, what is the probability that one of the dice rolled a 6?
2). In the game “raven’s beak,” a player rolls 6 dice, and wins if at least three of the dice roll the same number. What is the probability of winning?
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1). Two dice are rolled, and the results are added. Assuming
that this number is greater...
Two dice are rolled repeatedly until the sum of the two numbers rolled is 10 or...
Two dice are rolled repeatedly until the sum of the two numbers rolled is 10 or more. a) What is the probability that exactly 5 rolls are needed? (Count each time you roll the dice as one roll). b) What is the probability that more than 5 rolls are needed? c) Find the expected number of rolls.
9. In the casino dice game Craps, players make wagers on a sequence of rolls of...
9. In the casino dice game Craps, players make wagers on a sequence of rolls of a pair of dice. A sequence of rolls starts with the "shooter" making an initial roll of two dice called the "come-out” roll. If the sum of the dice on the initial roll is 7 or 11 then a player with a bet on the Pass Line wins. If the initial roll results in a sum of 2, 3, or 12 ("craps") then a...
Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability...
Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? (Hint: For each roll, two dice are rolled at the same time. It is considered as the success if at least one of two dice is 6 and as the failure if neither of dice is 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...
6.32 In the game of Chuck-a-luck, three dice are rolled. The player selects a number between...
6.32 In the game of Chuck-a-luck, three dice are rolled. The player selects a number between 1 and 6. If the player's number comes up on exactly one die, the player wins $1. If the player's number comes up on exactly two dice, the player wins $2. If the player's number comes up on all three dice, the player wins $3. If the player's number does not come up, the player loses $1. Let X denote the player's win or...
8. We roll two fair dice. (1) Given that the roll results in a sum of...
8. We roll two fair dice. (1) Given that the roll results in a sum of 6 or less, what is the conditional probability that doubles are rolled? A "double" means that two dice have the same number (2) Given that the two dice land on different numbers, what is the conditional proba- bility that at least one die roll is a 1?
In the game of Yahtzee®, players roll five dice simultaneously to try to make certain combinations....
In the game of Yahtzee®, players roll five dice simultaneously to try to make certain combinations. In a single turn, a player may roll up to three total times. On the first roll, the player rolls all five dice. On subsequent rolls, the player may choose to roll any number of the five dice ("keeping" dice by leaving selected unrolled dice on the table). If a player's first roll results in exactly three 5's (e.g., 2-5-5-3-5), what is the probability...
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...
Two strange dice (Die A and Die B) are rolled and their numbers showing are to...
Two strange dice (Die A and Die B) are rolled and their numbers showing are to be added together. Die A and one side that is a 1, while the other sides are 3’s. Die B has four sides that are 2’s and two sides that are 6’s. Complete this table showing the sample space for this event. + 1 3 3 3 3 3 2 2 2 2 6 6 P(sum of 5) = Using the same strange dice...
In Yahtzee, 5 standard dice are rolled up to three times on a given turn. A...
In Yahtzee, 5 standard dice are rolled up to three times on a given turn. A player can choose to save anywhere from 0 - 5 of the dice between rolls 1 and 2 and between rolls 2 and 3, meaning that the player can set aside certain dice before rolling the remaining dice if they choose to do so. Suppose that a given player does not take advantage of saving die rolls and instead rolls all 5 dice each...
9. In the casino dice game Craps, players make wagers on a sequence of rolls of a pair of dice. A sequence of rolls starts with the "shooter" making an initial roll of two dice called the "come-out” roll. If the sum of the dice on the initial roll is 7 or 11 then a player with a bet on the Pass Line wins. If the initial roll results in a sum of 2, 3, or 12 ("craps") then a...
Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? (Hint: For each roll, two dice are rolled at the same time. It is considered as the success if at least one of two dice is 6 and as the failure if neither of dice is 6.]
6.32 In the game of Chuck-a-luck, three dice are rolled. The player selects a number between 1 and 6. If the player's number comes up on exactly one die, the player wins $1. If the player's number comes up on exactly two dice, the player wins $2. If the player's number comes up on all three dice, the player wins $3. If the player's number does not come up, the player loses $1. Let X denote the player's win or...
8. We roll two fair dice. (1) Given that the roll results in a sum of 6 or less, what is the conditional probability that doubles are rolled? A "double" means that two dice have the same number (2) Given that the two dice land on different numbers, what is the conditional proba- bility that at least one die roll is a 1?
In the game of Yahtzee®, players roll five dice simultaneously to try to make certain combinations. In a single turn, a player may roll up to three total times. On the first roll, the player rolls all five dice. On subsequent rolls, the player may choose to roll any number of the five dice ("keeping" dice by leaving selected unrolled dice on the table). If a player's first roll results in exactly three 5's (e.g., 2-5-5-3-5), what is the probability...
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...
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