Two fair six-sided dice are rolled. Find the conditional probability of the event that the sum is six, given that the first die is odd. Are the two events independent?

Two dice are rolled at the same time. Find the probability of each event listed when the probability is given as P(die 1, die 2). For example, if you want to know the probability that you roll a 3 on the first die and and a 5 on the second die, it would be written as P(3, 5). Give your answer as a decimal rounded to the thousandth place (three numbers after the decimal). P(1, 1) = P(both odd) P(even, odd): P(2 anywhere) = P(sum of 8) = P(sum of 1) =

A pair of dice is rolled, and the sum of the faces is obtained. Find the probability that the sum is a multiple of 3.

Suppose that you repeatedly roll a pair of fair dice and keep track of the sum. What is the probability that you see a sum of 7 before you see an even sum 3 times? (In particular, you keep track of how many evens you roll, and you want the probability that you roll a 7 before you get to 3 evens.

Yahtzee is a game played with 5 dice. Players attempt to score points by rolling various combinations. When all dice show the same number, it’s called Yahtzee and scores 50 points for the first one and 100 points for each successive Yahtzee in the game. a. What is the probability that a person throws a Yahtzee on the very first roll? b. What is the probability that a person throws two Yahtzees on two consecutive rolls?

Find the probability that when a couple has six children. At least one of them is a boy. (Assume that boys and girls are equally likely)