Two machines turn out all the products in a factory, with the first machine producing 40% of the product and the second 60%. The first machine produces defective products 4% of the time and the second machine 7% of the time.(a) What is the probability that a defective part is produced at this factory given that it was made on the first machine?(b) What is the probability that a defective part is produced at this factory?

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Answered: Two machines turn out all the products…

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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Perform the experiment, tally your results, and calculate the probability.Simultaneously toss a coin and roll a die 100 times, and note the outcome of each trial. The possible outcomes are H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, and T6. Do these appear to be equally likely outcomes?
Two machines turn out all the products in a factory, with the first machine producing 35% of the product and the second 65%. The first machine produces defective products 4% of the time and the second machine 7% of the time. (a) What is the probability that a defective part is produced at this factory given that it was made on the first machine?(b) What is the probability that a defective part is produced at this factory?
In a certain town, males and females are 50% of the population. It is known that 20% of the males and 5% of the females are unemployed. A research student is studying the employment situation and randomly selects one person and found that the person was unemployed (i) Calculate the probability that the person selected was male. (ii) Calculate the probability that the person selected was female
Life insurance salesman meets his prospective customers separately. At each meeting, he makes the same effort to persuade the prospective client to be insured. The vendor's understanding after a long term in the insurance business is that the probability of persuading the customer to be insured (probability of success) is 0,1. What is the probability in 4 trials to insure one of them?
Peter oversees the electronics section of a large department store. He has noticed that the probability that a customer who is just browsing will buy something is 0.2. Suppose that 10 customers browse in the electronics section each hour. (i) What is the probability that no browsing customers will buy something during a specified hour? (ii) What is the probability that at least one browsing customer will buy something during a specified hour?
A baseballer rikes out 47% of the batters he faces (that is, the probability that he strikes out any given batter correct is .47). (a) In a series of five games, he faces 180 batters. What is the probability that he strikes out exactly 81 batters? (b) In a month, he faces 630 batters. What is the probability that he strikes out 310 or more batters? Now, every day for eternity he faces 100 batters, and records the number he strikes out. (c) Find the mean μ, and the standard deviation σ, of the numbers (of batters he strikes out on different days) that he records.

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