Two digital dice are rolled and a computer casino tells you at least one of the...
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?
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.
Conditional Probability Two fair dice are rolled: (a) Express the sample space S in set builder notation and the probability P "At least one of the dice rolls a four." Write all possible outcomes of A (b) Consider the event A (c) What is the probability that at least one die rolls a four? (d) What is the conditional probability that the first die rolls a four given that the sum of the dice is six? (e) What is the...
Two fair (6-sided) dice are rolled. If you are told that the two dice end up with two different face values, what is the probability that one die has a face value of 6?
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
(A) A pair of dice is rolled one time, what is the probability of getting sum of 8 or double. (B) A pair of dice is rolled 5 times, what is the probability of getting sum of 8 or double on all 5 rolls
Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? (Hint: For each roll, two dice are rolled at the same time. It is considered as the success if at least one of two dice is 6 and as the failure if neither of dice is 6.]
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?
9. In the casino dice game Craps, players make wagers on a sequence of rolls of a pair of dice. A sequence of rolls starts with the "shooter" making an initial roll of two dice called the "come-out” roll. If the sum of the dice on the initial roll is 7 or 11 then a player with a bet on the Pass Line wins. If the initial roll results in a sum of 2, 3, or 12 ("craps") then a...
If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the sum of the dice is i? Compute for all i = 2, 3, . . . , 12.