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?

We have to given that, Machine A, B, and C are did work 45% , 30% and 25% of total work…

Answered: In a fruit juice company, machine A…

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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4
Ms. Rasu designed a game where you roll a regular die with faces showing numbers 1, 2, 3, 4, 5, 6. If you roll a number that is a multiple of 3 you receive points double the amount of your roll, but if youroll any other number, you lose points the value of the roll. This information is recorded in the attached image.a) Complete the last column of the table.b) Calculate the expected value, E(X). c) Is this game fair? Justify.
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 7% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month?
A student will take two trainee selection exams for companies A and B, respectively. He estimates the probability that he will pass the exam.Company A's selection rate is 2/3. In company B, the probability of approval is 3/4. Finally, the probability of being approved in both processes simultaneously is of 50%. Under these conditions, what is the probability of passing only one of the companies?
A stock index consists of businesses in both Europe and the United States. Assume that each business comprising the stock index makes a profit or loss independently of the other businesses in the index. Suppose that an American business on the stock index makes a profit 60%60% of the time and a European business makes a profit 80%80% of the time. If there are 840 American businesses and 720 European businesses in the stock index, what is the expected number of businesses in the stock index to make a profit?
A major traffic problem in Baguio City can be seen in the intersection of Abanao and Maharlika. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.85 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes. Draw the transition diagram in 2 periods. (TREE DIAGRAM)
According to the Chronicles of Contrived Statistics (March, 2016), the probability that scientists from Area 51 will begin selling pet aliens in the next month is 38%. The probability that either Elon Musk will offer you a free trip to space or that scientists will begin sales of pet aliens next month is 59%. Finally, they list that probability of both happening in the next month is 25%. What is the probability that Elon Musk will offer you a free trip into space in the next month?
According to the Chronicles of Contrived Statistics (March, 2016), the probability that scientists from Area 51 will begin selling pet aliens in the next month is 21%. The probability that either Elon Musk will offer you a free trip to space or that scientists will begin sales of pet aliens next month is 55%. Finally, they list that probability of both happening in the next month is 22%. What is the probability that Elon Musk will offer you a free trip into space in the next month?
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 9% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)(a) in 1 month:nonsmokers:1 pack/day or less:more than 1 pack/day:(b) in 2 months:nonsmokers:1 pack/day or less:more than 1 pack/day:(c) in 1 year:nonsmokers:1 pack/day or less:more than 1 pack/day:
The Business School at State University currently has three parking lots, each containing 155 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, an average of 70% of all lot 1 parking sticker holders show up, an average of 72% of all lot 2 parking sticker holders show up, and an average of 74% of all lot 3 parking sticker holders show up. a. Given the current situation, estimate the probability that on a peak day, at least one faculty member with a sticker will be unable to find a spot. Assume that the number who show up at each lot is independent of the number who show up at the other two lots. Compare two situations: (1) each person can park only in the lot assigned to him or her, and (2) each person can park in any of the lots (pooling). (Hint: Use the RISKBINOMIAL function.) If needed, round your answer to a whole percentage and if your answer is zero, enter "0". No pooling: Pooling: 51.4 % 83.8 % b. Now suppose the numbers of people who show up at…

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