A player wants to roll a critical hit on his 20-sided dice (this means he rolls a 20). If he has a fair die, what is the expected number of rolls before he rolls a 20.
The solution to this problem is

A player wants to roll a critical hit on his 20-sided dice (this means he rolls...
In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is 16
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.
Roll 10 dice. Find probability sum of dice is 42. (dice are 6-sided. Min roll = 10. Max roll = 120.) (number of possible rolls = 6^10 = 60466176) = s^n number of favorable rolls = number of ways dice add to 42 [(number of favorable rolls)/(number of possible rolls)] = [Probability sum is 42] You must find number of favorable rolls. Given number of dice(n), sides(s), and sum of roll (r) as n = 10, s = 6, and...
The Dice game of "Pig" can be played with the following rules. 1. Roll two six-sided dice. Add the face values together. 2. Choose whether to roll the dice again or pass the dice to your opponent. 3. If you pass, then you get to bank any points earned on your turn. Those points become permanent. If you roll again, then add your result to your previous score, but you run the risk of losing all points earned since your...
A dice game is played with two distinct 12 sided dice. It costs $3 to roll the pair of dice one time. The payout scheme is as follows 1. Sum of 13 pays $10 Sum of 11 or 15 pays $6 Sum of 7, 9, 17, or 19 pays $3 Any other roll doesn't pay. What is the expected gain/loss after playing the game one time? A "fair" game is one in which the expected gain/loss after playing once is...
2. (25 points) Sekora International Casino (SIC) is launching a new game making use of fair 6-sided dice . In phase 1, roll two 6-sided dice and compute the difference between the rolls. Call this difference . In phase 2, roll r dice, and add up the total of the rolls. This is the payout in dollars of the game. (with the numbers 1-6 on the sides). The game proceeds in two phases as follows: (a) (5 points) In the...
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?
1. Suppose Jane has a fair 4-sided die, and Dick has a fair 6-sided die. Each day,they roll their dice (independently) until someone rolls a “1”. (Then the personwho did not roll a “1” does the dishes.) Find the probability that …a) they roll the first “1” at the same time (after equal number of attempts);b) it takes Dick twice as many attempts as it does Jane to roll the first “1”;c) Dick rolls the first “1” before Jane does.
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...
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?