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 even rolls in each outcome. For example, if the outcome is eoe, then N (eoe) = 2. Suppose that the random variable X is defined in terms of N as follows: X=N-1. The values of X are given in the table below. Outcome eoo ooo eeo ooe eee eoe oee oeo Value of X 0 -1 1 0 2 1 1 0 Calculate the probabilities P (X=x) 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(X=x) 0 0 0 0 0 0 olo

Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, three green ones, two white ones, and two purple ones. She grabs seven of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She has at most one green one.

A poker player holds a flush when all five cards in the hand belong to the same suit (clubs, diamonds, hearts, or spades). We will find the probability of a flush when five cards are drawn in succession from the top of the deck. Remember that a deck contains 52 cards, 13 of each suit, and that when the deck is well shuffled, each card drawn is equally likely to be any of those that remain in the deck.     The probability of drawing five spades in succession from the top of the deck is the product of the five probabilities you have found. Why? The probability of a flush in spades is the product of the probabilities due to the general multiplication rule which applies for determining the probability of dependent events occurring simultaneously. the multiplication rule for independent events which applies for determining the probability of at least one or more dependent events occurring. the general multiplication rule which applies for determining the…

Suppose you have three bowls, X, Y , and Z with some number of red and blue balls. Bowl X has 2 red and 2 blue balls, bowl Y has 1 red and 3 blue balls, and bowl Z has 3 red and 1 blue ball. A bowl is chosen at random and a ball is drawn from it. What is the probability that the ball was drawn from bowl X given the ball was blue?