Consider a collection of 18 color wheels, where each color wheelhas 6 colors: red, orange, yellow, green, blue, and purple. Assume furtherthat each color wheel has a spinner. On a given spin, each of the colorson a color wheel is equally likely to be spun, independent of the resulting4.color spun on any other color wheel.If each of the 18 color wheels is spun, what is the likelihood that orangeisspun on exactly 3 of the color wheels?LEERER

Given Data: n=18 p=1/6 X~ Binomial (18, 1/6)

Answered: 4. Consider a collection of 18 color…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In a random sample of 1,000 people, it is found that 7% have a liver ailment. Of those who have a liver ailment, 40% are heavy drinkers, 50% are moderate drinkers, and 10% are nondrinkers. Of those who do not have a liver ailment, 10% are heavy drinkers, 70% are moderate drinkers, and 20% are nondrinkers. If a person is chosen at random and he or she is a heavy drinker, what is the probability of that person having a liver ailment? What is the probability for a nondrinker?
30. The chess clubs of two schools consists of, respectively, 8 and 9 players. four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that exactly one of Rebecca and Elise will be chosen to represent her school? Show the STEP-BY-STEP SOLUTION CLEARLY. SHOW EXPLAMATIONS IF NECESSARY.
Suppose a computer company has manufacturing plants in three states. 50% of its computers are manufactured in Califomia, and 85% of these are desktops; 30% of computers are manufactured in Washington, and 40% of these are laptops; and 20% of computers are manufactured in Oregon, and 40% of these are desktops. All computers are first shipped to a distribution site in Nebraska before being sent out to stores. If you picked a computer at random from the Nebraska distribution center, what is the probability that it is a laptop?
Suppose that we've decided to test Clara, who works at the Psychic Center, to see if she really has psychic abilities. While talking to her on the phone, we'll thoroughly shuffle a standard deck of 52cards (which is made up of 13 hearts, 13 spades, 13 diamonds, and 13 clubs) and draw one card at random. We'll ask Clara to name the suit (heart, spade, diamond, or club) of the card we drew. After getting her guess, we'll return the card to the deck, thoroughly shuffle the deck, draw another card, and get her guess for the suit of this second card. We'll repeat this process until we've drawn a total of 14 cards and gotten her suit guesses for each.Assume that Clara is not clairvoyant, that is, assume that she randomly guesses on each card. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution (that is, the expectation of…
6.) A mathematics class has 16 engineers majors, 12 science majors, and 4 liberal artsmajors.a.) What is the probability that a student selected at random will be a science orliberal arts major?b.) What is the probability that a student selected at random will be anengineering or science major?c.) 5 of the engineering students, 6 or the science majors, and 2 of the liberal artsmajors are female. What is the probability that a student selected at random is anengineering major or a female?
Urn A has five mauve marbles, seven burnt sienna marbles, and three puce marbles. Urn B has seven mauve marbles, two burnt sienna marbles, and three puce marbles. First, a random marble is transferred from Urn A to Urn B. Then two marbles are drawn from Urn B simultaneously. What is the probability that the two marbles are the same color?
8. The composition of the 108th Congress is 50 Republicans, 48 Democrats, and 2 Independent. A committee on aid to higher education is to be formed with 3 Senators to be chosen at random to head the committee. Find the probability that the group of 3 consists of a. All Democrats b. One Democrat, one Republican, and one Independent
Suppose that we've decided to test Clara, who works at the Psychic Center, to see if she really has psychic abilities. While talking to her on the phone, we'll thoroughly shuffle a standard deck of 52 cards (which is made up of 13 hearts, 13 spades, 13 diamonds, and 13 clubs) and draw one card at random. We'll ask Clara to name the suit (heart, spade, diamond, or club) of the card we drew. After getting her guess, we'll return the card to the deck, thoroughly shuffle the deck, draw another card, and get her guess for the suit of this second card. We'll repeat this process until we've drawn a total of 14 cards and gotten her suit guesses for each. Assume that Clara is not clairvoyant, that is, assume that she randomly guesses on each card. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution (that is, the expectation of the relevant…

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