Question 3: Conditional probability, Bayes' theoremIn a fruit juice company, machine A (crusher) produces 45%,Machine B (juice extractor) produces 30%, and Machine C(filler) produces 25% of the total work for fruit juice in a factoryon a given day. The defective output of these machines is 1%,2% and 4%, respectively.a) Draw the tree diagram with detailed descriptions on thebranches (including the probability for each branch).b) If a can of juice is selected at random, find the probabilityof the event A that the can is defective.c) If a can of juice is selected at random and is found to bedefective, what is the probability that the can was filled byMachine C?

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Answered: Question 3: Conditional probability,…

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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1. Consider the gambler's ruin problem. Alice starts with £a; her opponent Bob starts with £(ma). In each round, Alice wins £1 from Bob with probability p, or loses £1 to Bob with probability q = 1 - p. Alice ruins if she is reduced to £0; Bob ruins if he is reduced to £0, which means Alice would have £m. Let X denote the amount of money in pounds that Alice has after n rounds. Consider the stochastic process (✗n). pri+1ri+gri-1 = 0 for i = 1, 2,..., m — 1, Assuming p, solve the linear difference equation in part (c), to show that the ruin probability is pm - pa ra pm 1 ' where you should identify p in terms of p and q.
Please show your answer and explain it. DO ONLY PROBLEM 53
Problem 3. On average there are four traffic accidents in a city during one hour of rush-hour traffic. Use the Poisson distribution to calculate the probability that in one such hour there are a) No accidents b) At least five accidents.
QUESTION 3 H Profits for a skiing resort depends on how much snow falls in winter. The probability distribution of snowfall and resulting profitability is as follows: More than 40 inches K120 000 40% 20 to 40 inches K40 000 20% Less than 20 inches -K40 000 40% The owner receives an offer from a hotel chain to lease the resort at a guaranteed profit of K45 000 for the season. He is also considering leasing snow making equipment which would allow the resort to operate full-time regardless of the amount of natural snow fall which would ensure profit of K120 000 minus the cost of leasing and operating the snow equipment. The leasing cost is K12 000 per season regardless of usage. Operating cost will be K10 000 for natural snowfall of more than 40 inches, K50 000 for between 20 and 40 inches and K90 000 if it is less than 20 inches. Required: Construct a decision tree…
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Rework problem 21 from section 4.1 of your text involving the deep-sea fisherman. Assume that the fisherman can use between 5 and 8 lines. With 5 lines, the probability of a catch on each line is 0.77. With 6 this probability is 0.66, with 7 it is 0.52, and with 8 the probability is 0.49. How many lines should the fisherman use to maximize the probability of catching at least 3 fish?
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Question 2) Waiting Line Analysis A customer service desk with 1 worker is able to process an average of 9 customer inquiries per hour. An average of 6 customers arrive for help at the desk each hour. c) What is the average time required to serve a customer (in minutes)? d) What is the probability that more than 2 customers will arrive in the next hour?
Section 5.3 A computer software company receives hundreds of support calls each day. There are several common installation problems, call them A, B, C, and D. Several of these problems result in the same symptom, lock up after initiation. Suppose that the probability of a caller reporting the symptom lock up is 0.6 and the probability of a caller having problem A and a lock up is 0.5. Step 1 of 2 : Given that the caller reports a lock up, what is the probability that the cause is problem A? Round your answer to four decimal places, if necessary. Step 2 of 2 : What is the probability that the cause of the malfunction is not problem A given that the caller is experiencing a lock up? Round your answer to four decimal places, if necessary.
Question 9 Suppose events A, B, and C are independent and P(4) = P(B)= P(C)= 42 Find the probability P(AUB). Edit View Insert Format Tools Table 12pt v Paragraph v BIUA
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