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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C1. A collector wants to collect football stickers to fill an album. There are n unique stickers to collect. Each time the collector buys a sticker, it is one of the n stickers chosen independently uniformly at random. Unfortunately, it is likely the collector will end up having "swaps", where he has received the same sticker more than once, so he will likely need to buy more than n stickers in total to fill his album. But how many? (a) Suppose the collector has already got j unique stickers (and some number of swaps), for j = 0, 1, 2, . . .‚ n – 1. Let X, be the the number of extra stickers he buys until getting a new unique sticker. Explain why X, is geometrically distributed, and state the parameter p = p; of the geometric distribution. (b) Hence, show that the expected number of stickers the collector must buy to fill his album is n n k=1 k (c) The World Cup 2020 sticker album required n = 670 unique stickers to complete it, and stickers cost 18p each. Using the expression from…
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.)
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.
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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