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 cent)? Is this a fair game?
(B) For what value or values of k is this game fair?
In a dice game, you roll a fair die three times, independently. If you don’t roll...
The following dice game is offered to you. You may simultaneously roll one red die and three blue dice. The stake is $1. If none of the blue dice matches the red die, you lose your stake; otherwise, you get anyway paid k + 1 dollars if exactly k of the blue dice match the red die. In the case that exactly one blue die matches the red die, you get paid an additional $0.50 if the other two blue...
. 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?
In a dice game, the player independently rolls a fair red die and a fair green die.The player wins if and only if the red die shows a 1, or 2, or 3, or if the total on the two dice is 11. What is the probability the player will win?
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 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
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...
You are playing a gambling game with a 12-sided die. If you roll an odd number, then you lose $6. If you roll an even number, then you win that amount in dollars (i.e., you roll a 2, you win $2, etc). What is the Expected average winnings/losings of this game? x = die roll P(x) Payoff(x) P(x)*Payoff(x) 1 2 3 4 5 6 7 8 9 10 11 12 E =
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
Suppose you roll a pair of fair dice 10 times. What's the probability that you'll roll a "7" exactly twice? Choose the best answer. ))() X
You have two fair six-sided dice and you roll each die once. You count the sum of the numbers facing up on each die. Let event A be "the sum is not a prime number." What is P(A) 06/12 06/11 05/11 05/12