4. Dice #1 is rolled a single tine. Dice #2 is rolled repeatedly. The game stops...
4. Dice #1 is rolled a single time. Dice #2 is rolled repeatedly. The game stops at the first time that the sum of the two dices is 4 or 7. What is the probability that the game stops with a sum of 4?
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.
Problem 9 A single game of craps (a dice game) consists of at most two rolls of a pair of six sided dice. The ways to win are as follows: Win-the first roll of the pair of dice sums to either 7 or 1 (you win, game over, no second roll Win the first roll of the pair of dice does NOT sum to either 7 or 1 but the sum of the second roll is equal to the sum...
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...
Two distinct dice will be rolled until the first time the sum on the two dice is seven. What is the probability that this will happen at the fourth roll?
Rolling Dice 2. A pair of dice is rolled. Here is the sample space (all of the possible outcomes) of rolling a pair of dice. First Die a) In how many different ways can we roll a 7 (as the sum of the two dice)? What is the probability of rolling a 7? 2 3 4 5 6 7 3 4 5 6 7 8 b) In how many ways can we roll a sum that is divisible by 3?...
SectionA Q1. a. Two dice are rolled repeatedly until their scores, Χ, and X, differ by at least two. Find: (i) The probabilities of all possible values of the sum of the scores X, + X2. (i) The marginal probability of all values of X. b. Adice is rolled repeatedly until the total score of all the rolls is at least six. This takes K rolls. Find (i) The probabilities of all possible values of K. (i) The expected value...
1. A blue fair 6-sided dice and a red fair 6-sided dice are rolled at the same time. a) What is the probability of the sum of the dice equals 7, given 1 2 3 4 5 6 at least one of the dice shows a 3? 1 (1.1) (1.2) (1.3) (1.4) (1.5) (1.6) 2 (2.1) (2.2) (2.3) (2.4) (2.5) (2.6) (3.1) (3.2) (3.3) (3.4) (3.5) (3.6) (4.1) (4.2) (4.3) (4.4) (4.5) (4.6) 5 (5.1) (5.2) (5.3) (5.4) (5.5) (5.6)...
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?
7. Rolling Two Dice If two dice are rolled one time, find the probability of getting these results. a. A sum of 10 b. A sum of 6 or 11 c. Doubles and sum less than 6