. Three Dice of a Kind
Consider the following game: You roll six 6-sided dice d1,…,d6 and you win if some number appears 3 or more times. For example, if you roll:
(3,3,5,4,6,6)
then you lose. If you roll
(4,1,3,6,4,4)
then you win.
What is the probability that you win this game?
. Three Dice of a Kind Consider the following game: You roll six 6-sided dice d1,…,d6...
Consider the following game: You roll six 6-sided dice dı,..., de and you win if some number appears 3 or more times. For example, if you roll: (3,3,5,4,6, 6) then you lose. If you roll (4,1,3,6,4,4) then you win 1. What is the probability that you win this game? Hint: The answer is 119/324
Consider a game where you roll a six-sided die and a four-sided die, then you subtract the number on the four-sided die from the number on the six-sided die. If the number is positive, you receive that much money (in dollars). If the number is negative, you pay that much money (in dollars). For example, you might roll a 5 on the six-sided die and a 2 on the four-sided die, in which case you would win $3. You might...
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...
Here is a version of the game of crap. First, you roll two well-balanced, six-sided dice; let x be the sum of the dice of the first roll. If x = 7, or x = 11 you win, otherwise you keep rolling until either you get x again, in which case you also win, or until you get a sum of 7 or 11 in which case you lose. Write a function that takes no input, and simulate the game...
(A) If you roll 3 six-sided dice, what is the probability of getting an overall score of 8? (B) If you roll 3 six-sided dice 4 times, what is the probability of getting an overall score of 8 four times in a row? (C) If you roll 3 six-sided dice 2 times, what is the probability of getting an overall score of 8 on the first roll and an overall score of 3 on the second roll?
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...
In the game of "Craps", a roller plays by rolling two six-sided dice. The score for each roll is the sum of the two dice. A roller can win on the first roll by rolling either a sum or 7 or 11. The probability of this occurring can be found using the sample space to be 0.2222. This probability (0.2222) is an example of what type of probability? O Theoretical Probability O Empirical Probability O Sample Probability There is not...
A friend bets you $100 on a game involving two six-sided dice, one red and one green. You choose the number of times the pair of dice will be rolled. You win if the number of times a red 6 is rolled is at most 2 and the number of times a green 6 is rolled is at least 2. a) How many times should the dice be rolled to maximise your chance of winning? b) With that number of...
You play a game in which you roll a number n of dice. You win if you roll at least one 6, but no 1s or 2s; and, otherwise, you lose. What is the optimal number of dice to roll in this situation? Choose the best answer. A) 1 B) 2 C) 3 D) 4
1. (25 points 6+6+6+7) For a fair throw of six 6-sided dice (as in the game Farkle): (a) Find the probability of 6 of a kind ANSWER (b) Find the probability of two different triplets. ANSWER (c) Find the probability of a four-of-a-kind and a different pair. ANSWER: (d) Now suppose the six dice are each of a different color and all placed an urn. After having chosen 4 with replacement, find the probability that two or more colors are...