A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability.For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.Outcomes ProbabilityEEE EOO OEE OEO EEO EOE OOO OOEEvent A: No even numbers on the last two rolls 18Event B: Two or more even numbers 12Event C: An even number on the second roll or the third roll (or both) 34

A number cube with faces labeled 1 to 6 is rolled once.The number rolled will be recorded as the outcome.Consider the following events.Event A: The number rolled is even.Event B: The number rolled is greater than 3.Give the outcomes for each of the following events.If there is more than one element in the set, separate them with commas.(a) Event"AandB":(b) Event"AorB":(c) The complement of the event B:

A fair number cube is rolled. What are the odds in favor of rolling a 1?

An number cube (a fair die) is rolled 3 times. For each roll, we are interested in whether the roll comes up even or odd. An outcome is represented by a string of the sort oee (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll).For each outcome, let N be the random variable counting the number of odd rolls in each outcome. For example, if the outcome is oeo, then =Noeo2. Suppose that the random variable X is defined in terms of N as follows: =X−2N2−4N3. The values of X are given in the table below.Outcome ooo eoe eeo oeo ooe eee eoo oeeValue of X 3 −5 −5 −3 −3 −3 −3 −5Calculate the probabilities P=Xx of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.Value x of X P=Xx

A six-sided cube is rolled. What is the probability that the number is odd or less than 4?Event A: Numbers on a six-sided cube are odd: 1, 3, 5Event B: Numbers on a six sided cube are less than 4: 1, 2, 3 1/2 2/3 5/6 1

You roll two number cubes.Let event A = You roll an even number on the first cube.Let event B = You roll a 2 on the second cube.Are the events independent or dependent? Why?A.Independent, because they have no outcomes in common.B.Dependent, because 2 is an even number.C.Dependent, because both cubes have six sides.D.Independent, because the outcome of the first roll doesn't affect the outcome of the second roll.