89. A factory has two machines A and B. Past records show thatmachine A produces 30% of the total output and machine B the remaining 70%.Machine A produces 5% defective articles and machine B Produces 1%defective items. An item is drawn at random and found to be defective. What isthe probability that it was produced (a) by machine A (b) by machine B.

Answered: 89. A factory has two machines A and B.…

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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8. In a science class, the grades of a test and gender are summarized below. If one student is chosen at random, find the probability that (a) the student is female and earned an A. (b) the student is female or earned a B. (c) the student is male. (d) the student is female given that the student earned an A. (e) the student got an A given that it is a male student. A B C Total Male 8 18 13 33 Female 10 4 12 48 Total 18 22 25 81
Urn A contains six white balls and three black balls. Urn B contains seven white balls and five black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was black given that the second ball drawn was black? (Round your answer to three decimal places.)
3. A group of people were asked if they had run a red light in the last year. 150 responded “yes”, and 185 responded “no”. Find the probability that if a person is chosen at random, they have run a red light in the last year.
6. Machines A and B produce 40% and 60%, respectively of the production of a component intended for the electronics industry. From experience, it is known that the probability that machine A produces a defective component is 0.015 while the probability that machine B produces a defective component is 0.025. If a component is selected at random from a day's production, find the probability that the component is defective. а. b. If a component is selected at random from a day's production and is found to be defective, use Bayes' theorem to find the probability that it is made by machine A.
Suppose that 57% of people own dogs. If you pick two people at random, what is the probability that they both own a dog? Give your answer as a decimal (to at least 3 places) or fraction
4. At a High school, 70% of the seniors have taken an advance calculus course. Of those who have taken Advanced Calculus, 60% will apply for a Pre-Health science major when they apply for college admission. Of those who have not taken advanced calculus, 40% will apply for a Pre-Health science major when they apply for college admission. A senior is selected at random. What is the probability that the senior have taken advanced calculus, given that the senior will apply for a pre-health science major?
Urn A contains five white balls and three black balls. Urn B contains seven white balls and four black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was black given that the second ball drawn was black? (Round your answer to three decimal places.)
Suppose 33.3% of high school students eat pizza and 42% drink soda. If 17.3% of high school students eat pizza and drink soda, what is the probability that a randomly chosen high student will either eat pizza, drink soda, or both?
1. At some random moment, Ethan looks at his watch and note the minutes reading. What is the probability that the minutes reading is 15? A. 1/60 b. 1/45 c. 1/30 d. 1/15 2. In a 200-ticket draw for a grocery package, Terry's name was written on 100 tickets. What is the probability that she will win? A. 1/2 B. 1/4 C. 1/6 D. 1/8 3. What is the probability of getting blue paper star if there are 10 blue paper stars in the 50 different colored paper stars inside the box? A. 1/2 B. 1/3 C. 1/4 D. 1/5 please answer it all, thank you.
3. A retailer sells two brands of batteries that experience indicates are equal in demand. If he stocks two of each brand (which means he has 4 batteries in his store), what is the probability that a customer seeking to purchase two batteries, purchases the same brand? 1/3 2/3 01/2 1/4
A math class consist of 25 students , 14 female and 11 male. Three students are selected at random to participate in a probability experiment. Compute the probability that a. A male is selected , then two females b.a female is selected, the two males c. Two females are selected, then one male d. Three male are selected e. Three females are selected
6) Medical researchers know that the probability of getting lung cancer if a person smokes is 0.34. The probability that a nonsmoker will get lung cancer is 0.03. It is also known that 11% of the population smokes. What is the probability that a randomly selected person is both a smoker and gets lung cancer? A. 0.037 B. 0.324 C. 0.340 D. 0.230 E. None of the above.

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