A manufacturer of bicycles produces 80 per cent of its output in its New York factory and the rest in SanFrancisco. If the probability of a defect in its New York output is 5% and the defect rate is 2% in SanFrancisco.(i)What is the probability a defective product was manufactured in San Francisco?(ii)If the firm replaces all defective bicycles, how many replacements will be required out of theweekly sales of 2000 bicycles?

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Answered: A manufacturer of bicycles produces 80…

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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Charlie buys a one-year term home insurance policy for $p, that will pay $200,000 in the event of a major catastrophe and $35,000 in the event of a minor catastrophe. Charlie's home has a 0.2% chance of a major catastrophe and a 0.7% of a minor catastrophe during the one year term. What did the insurance company charge Charlie for this policy if the company expected to break even?
The 10-year survival rate for blood cancer is approximately 12%. If 145 people who have blood cancer are treated for the disease, calculate the probability that: (i) no one will survive for 10 years. (ii) not more than 4 will survive for 10 years.
Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flying over similar distances in flatter portions of the nation, according to a General Accounting Office study completed in response to a congressional request. The accident rate for small aircraft in the 11 mountainous western states is 2.5 accidents per 100,000 flight operations. (b) Find the probability of no accidents in 100,000 flight operations. (Use 4 decimal places.)(c) Find the probability of at least 8 accidents in 200,000 flight operations. (Use 4 decimal places.)
(a) Student A would like to visit a country where 92% of the population speaks the native language. However, Student A does not speak and understand that language. What is the probability that at least two of three locals at the immigrant department of the airport will succeed to communicate with Student A? Answer = Answer (b) Research Scientist A investigates the infected laboratory rats in modeling human diseases. Research Scientist A finds out the probability of the laboratory rats getting infected is two out of ten. What is the probability that five laboratory rats must be required before Research Scientist A finds at least three laboratory rats but not all have been infected? Answer = Answer (c) A badminton game consists of at least two matches, and each match consists of 21 points. The probability of Player A and Player B earning a point in their matches are 80% and 90%. What is the probability difference between Player A and Player B to get their second points within…
Your car is making a funny noise. You believe that the problem is either with the wheel or the axle, and you believe the probability is 0.3 that the wheel needs to be replaced, and 0.7 that the axle needs to be replaced. You need to decide whether to replace the wheel or the axle first. The cost of each alternative is given in the following table (if you decided to replace the wrong part first, you have to replace both of them). The Wheel is broken p = 0.3 The Axle is broken p = 0.7 Replace Wheel First Replace Axle First 600 1500 1500 900 a) Find the EV of each decision alternative. Which part should you replace first? b) What is the EVPI?
What is the probability of finding an H2O based compound with a blue label in a storage facility of 1,000 vials. We know there are 22 vials of H2O based compound in the facility, and that 800 of the total number of vials in the facility have blue labels.
In automotive repair, experience has shown that a rough - running engine can be attributed to the bad ignition wires 35% of the time, bad spark plugs 80% of the time, and both problems 20% of the time. Suppose a mechanic begins to diagnose the problem by checking the spark plugs first and find them to be bad. Given this information, what is the probability that the wires are also bad?
In a recent year, the percentage of patients at a doctor's office who received a flu shot was 60%. A campaign by the doctors and nurses was designed to increase the percentage of patients who obtain a flu shot. The doctors and nurses believed there was an 80% chance that someone who received a shot in year 1 would obtain a shot in year 2. They also believed that there was a 40% chance that a person who did not receive a shot in year 1 would receive a shot in year 2. Complete parts (a) through (c) below. (a) Give the transition matrix for this situation. Set up the transition matrix P so that the first row and first column represent obtaining a flu shot and the second row and second column represent not obtaining a flu shot. P = (Type an integer or decimal for each matrix element.)
Q. 2 The probability that a smoker who consumes over 20 cigarettes a day will suffer from chronic respiratory illness is 4 The 10 probability that he will suffer from heart disease is The 10 probability that he will suffer from at least one of these ailments is 6.5 10 (i) Find the probability that the smoker will suffer from both ailments. (ii) Find the probability that he will suffer from heart disease given that he suffers from chronic respiratory illness. (iii) Find the probability that he will suffer from chronic respiratory illness given that he suffers from heart disease. (iv) Are events "chronic respiratory illness" and "heart disease independent"?
2. Wallace figures his chances of getting a new car for graduation at 70% if he graduates as class valedictorian. He only has about a 25% chance of getting a new car if he graduates 2nd or lower. He estimates his chances of being valedictorian at 50/50. What is the likelihood that Wallace will get a new car?
If Johnny plays Russian Roulette twice, by spinning a revolver containing one bullet in one of the six chambers between each shot, what is the probability he doesn't shoot himself either time?
the sales manager knows that 10% of his clients do not pay their debts in full. He supposes that he selects a sample of 100 clients. What is the probability that 14% or more will not be fulfilled in their obligations?

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