1. (25 points 6+6+6+7) For a fair throw of six 6-sided dice (as in the game...
Suppose that you roll 112 fair six-sided dice. Find the probability that the sum of the dice is less than 400. (Round your answers to four decimal places.)You may need to use the appropriate table in the Appendix of Tables to answer this question.
. 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?
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?
2. Suppose you have a four-sided dice, a six-sided dice and a 12-sided dice, each dice is fair. You roll the three dice once and let Z be the number of 4's showing. Find E(Z) using the indicator method.
1. Suppose 7 dice are rolled. The dice are 6-sided and fair. a). Find the probability that more than 5 dice show 2 or less (you may leave your answer in unsimplified form). I found this answer to be 5/729= 0.006859 b). Suppose we roll 7 dice and count the number showing 2 or less. We repeat this experiment over and over, each time counting the number showing 2 or less. What should we expect to compute as an average...
Three fair six-sided dice are rolled. a) What is the probability of seeing {1, 3, 6}? b) What is the probability of seeing {1, 4, 4}? c) What is the probability of seeing {2, 2, 2} ? d) What is the probability of seeing at least one 6? e) What is the probability that the sum of all three dice is 16? f) What is the probability of seeing exactly two even numbers?
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...
1.) Suppose you roll two fair six-sided dice. What is the probabilty that I rolled a total of 5? 2.) Suppose you roll two fair six-sided die and I announce that the sun of the two die is 6 or less. What is the probabilty that you rolled a total of 5?
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...
Fair diced, which is unbiased. Each throw is independent. Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y], rounded to nearest .xx.