1. A garlic press factory has four machines turning out garlic presses. Machine 1 makes 35% of the totaloutput, and 5% of the presses turned out by machine 1 are defective. Machines 2, 3, and 4 make30%, 20%, and 15% of the total output, and their percentages of defective presses are 4%, 2% and 2%respectively. Let events M₁, M2, M3, and M4 represent the machine the press came from, and let eventD represent a defective garlic press. Find the following probabilities, building up to using Bayes' rule:a) P(M₁), P(M₂), P(M3), and P(M₁)b) P(DM₁), P(D|M2), P(D|M3), and P(DM₁)c) Use Bayes rule, and all of the probabilities above to find P(M3|D)

Given that, The event M1 is the press came from machine 1 The event M2 is the press came from…

Answered: 1. A garlic press factory has four…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You randomly select two poker chips from a bag containing 7 poker chips: 4 red, 1 blue, 1 green, and 1 white. Compute the following events: Event A: You select a green poker chip Event B: You select two poker chips that are the same color. Is the following statement true or false? Events A and B independent.
Help!!
Recently, Hector ran for president of the local school board. Of those who voted in the election, 80% had a high school diploma, and the other 20% did not. Hector got 65% of the vote of those with high school diplomas, while he got only 25% of the vote of those without high school diplomas. Let D denote the event that a randomly chosen voter (in the school board election) had a high school diploma and D denote the event that a randomly chosen voter did not have a high school diploma. Let H denote the event that a randomly chosen voter voted for Hector and H denote the event that a randomly chosen voter did not vote for Hector. Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses. (If necessary, consult a list of formulas.)
A group of fifteen tourists is stranded in a city with four hotels of the same class. Each of the hotels has enough room available to accommodate the fifteen tourists. The group's guide, who has a good working relationship with each of the four hotels, assigns the tourists to the hotels as follows. First, he randomly determines how many are to go to hotel A, then how many of the remaining tourists are to go to hotel B, and then how many are to go to hotel C. All remaining tourists are sent to hotel D. Note that each stage of the assignment the guide draws at random a number between zero and the number of tourists left. What is the probability that all four hotels receive guests from the group?
In a soon to be released Halloween martial arts movie, a pumpkin has a starring role. Because of the rather violent nature of the film, the producers have also hired a stunt pumpkin. Suppose the featured pumpkin appears in 40% of all the film scenes, the stunt pumpkin appears in 30% of the film scenes and the two appear simultaneously in 5% of the scenes. Draw the Venn diagram to reflect information given in the problem. Are the events the stunt pumpkin appearing in a scene and the featured pumpkin appearing in a scene mutually exclusive (disjoint)? Explain how you know. Are the events the stunt pumpkin appearing in a scene and the featured pumpkin appearing in a scene independent? Explain how you know. What is the probability that in a given scene that only the stunt pumpkin appears? You have three events A, B, & C. Suppose: Event A is the event of drawing a king from a deck of 52 cards on the first draw. Event B is the probability of drawing a queen of hearts on the…
event. The first card is a club and the second is a spade.
5. Consider a bag of marbles, 19 of which are green, 25 of which are blue, and 6 of which are red. Moreover, suppose 9 of the green marbles are opaque, 5 of the blue marbles are opaque, and 3 of the red marbles are opaque, and the rest of the marbles are transparent. Suppose you draw one marble from the bag and let G, B, and R be the events that the marble is green, blue, and red, respectively, and let O be the event that it is opaque. (a) Find P(RO). (b) Find P(R|Oº). (c) Find P(R). (d) Check whether R and O are independent. (e) Find P(BO). (f) Find P(OG). (g) Find P(BUGIO).
2. A group of three undergraduate and six graduate students are available to fill certain student government posts. If four students are randomly chosen from this group, find the probability that exactly two undergraduates will be among the four chosen. [Hint: How many ways are there to fill the posts? How many ways satisfy the condition of having exactly TWO undergraduates selected AND hav- ing exactly two graduates selected?]
5. A group of n people stand in a line. On the count of three, each of them simultaneously chooses to look either left or right (with equal probability): at one of their neighbors. Let X be the number of pairs of adjacent people that end up facing each other. (For example, if n = 5 and the random facings are "Left, Left, Right, Left, Right" then only the 3rd and 4th people face each other.) (a) Find the expected value E[X]. (b) Find Pr[X=0]. (c) Assuming n is even, find the maximum possible value of X, and the probability that X is equal to that value.
Five people, designated as A,AB,C,D,E are arranged in linear order. Assuming that each possible order is equally likely, what is the probability that there are exactly two people between A and B?
A company buys microchips from three suppliers—I, II, and III. Supplier I has a record of providing microchips that contain 10% defectives; Supplier II has a deflective rate of 5%; and Supplier III has a defective rate of 2%. Suppose 20%, 35%, and 45% of the current supply came from Suppliers I, II, and III, respectively. If a microchip is selected at random from this supply, what is the probability that it is defective?
1. A realtor sells houses in three different neighborhoods in the city—A, B and C. He sells ranch style homes and two-story homes. Last year, 60% of his sales were in neighborhood A, while neighborhood B made up 25% and neighborhood C was 15% of the sales. Only 10% of the houses in neighborhood A were ranches, compared with 40% for neighborhood B and 50% for neighborhood C. Suppose we randomly select one of the homes he sold in one of these three neighborhoods. (1) What’s the probability that the home is a ranch? (Enter a decimal as your answer, round to the nearest thousandth when necessary) (2) If the home is a ranch, what’s the probability that it is in neighborhood C? (Enter a decimal as your answer, round to the nearest thousandth when necessary)

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