Define Bayes theorem. The stock of a warehouse consists of boxes of high, medium and low quality light bulbs in respective proportions 1:2:2. The probability of bulbs of three types being unsatisfactory are 0.0, 0.1, and 0.2, respectively. If a box is chosen at random and two bulbs in it are tested and found to be unsatisfactory, what is the probability that it contains bulbs (i) of high quality, (ii) of medium quality, (iii) of low quality

Define Bayes theorem. The stock of a warehouse consists of boxes of high, medium and low quality light bulbs in respective proportions 1:2:2. The probability of bulbs of three types being unsatisfactory are 0.0, 0.1, and 0.2, respectively. If a box is chosen at random and two bulbs in it are tested and found to be unsatisfactory, what is the probability that it contains bulbs (i) of high quality, (ii) of medium quality, (iii) of low quality

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...

See similar textbooks

Similar questions

27273)3$4$44$4)
4 children. He makes a fast, wrong estimate of the probability of various mixes of boys and girls among QUESTION 3. Mr. Fastwrong is working for the census department and he is counting families that have the families. His assistant, Ms. Slowright, analyzes the issue and corrects his work. Fill her corrections of his wrong guesses into the table below. Number of boys among the 4 children 1 0 4 3 2 Number of girls among the 4 children 0 1 2 4 Use fractions (not percents) in your answers. Mr. Fastwrong's estimate of the fraction of families having this distribution of boys and girls 1/5 1/5 1/5 1/5 1/5 Ms. Slowright's estimate of the fraction of families having this distribution of boys and girls
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…
A random sample of 250 students majoring in Psychology or Communication at a largeuniversity is selected. These students are asked whether or not they are happy with theirmajors. The results of the survey are displayed in the following table. We assume herethat none of these students is majoring in both areas.Happy UnhappyPsychology 80 20Communication 115 35If a student is randomly selected from this group of 250 students, find the probabilitythat this student is(a) Happy with the choice of major(b) In Psychology major(c) In Communication major, given that the student is happy with the choice of major.(d) Unhappy with the choice of major, given that the student is in Psychology major(e) In Psychology major and is happy with that major(f) In Communication major or is unhappy with his or her major.
If a coin is balanced so that p(Heads) = p(Tails) = 1/2, then which of the following outcomes is least likely to occur? Select one: a. 10 Heads in 10 tosses b. 8 Heads in 10 tosses c. 2 Heads in 10 tosses d. 5 Heads in 10 tosses
Suppose that the proportions of blood phenotypes in a particular population are as follows: O A B AB 0.47 0.06 0.02 0.45 Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? (Enter your answer to four decimal places.) What is the probability that the phenotypes of two randomly selected individuals match? (Enter your answer to four decimal places.)
Which of the following statements is true? Question 9 options: It is possible for a distribution to have two means. It is possible for a distribution to have two medians. It is possible for a distribution to have two modes. It is possible for a distribution to have two medians or two modes.
20. A milk vendor sells sweetened milk after bottling it. He is assurea of selling 40 bottles every day to his regular customers while the maximum number he could sell is 80 bottles. On the be ..is of his experience he calculated the probability of demand per day as follows : Demand (bottles) 40 50 60 70 80 Probability of Demand 0-1 0-2 0-4 0-2 0-1 Miik costs him Rs. 8 per litre and he spends Rs. 4 per litre for sweetening and on overheads. After bottling it in 250 ml bottles he sells it for Rs. 8 per bottle. If any bottle remains unsold at the end of the day, the contents are thrown away. If any day's demand is independent of the previous day's, what is the optimum number of bottles he should stock every day ? Find the maximum expected profit for this order.
3. Daily demand for lots of apples at the grocery store is given by the following probability distribution: 10 15 20 p(x) |0.30 0.55 0.15 The store buys a lot for $55 and sells it for $130 each. Any unsold lots at the end of the day are disposed at $45 each. Assuming that the stock level is restricted to one of the demand levels, how many lots should be stocked daily?
5. A commuter must pass through 4 different traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below.X P(X) 0 0.05 1 0.25 2 0.35 3 0.20 4 0.15a. What is the probability she is stopped one time on her way to work?b. What is the probability she is stopped at least two times on her way to work
A system consists of four components connected as shown below in the following diagram.Assume ?, ?, ?, and ? function independently. If the probability that ?,?, ?, and ? fail are 0.10, 0.05, 0.10, and 0.20 respectively. What is the probability that the system functions?b) A process manufactures ball bearing whose diameters are normally distributed with mean 2.505?? and standard deviation 0.008??. Specifications call for the diameter to be in the interval 2.5 ± 0.01 cm. what proportion of the ball bearings will meet the specification
Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results are summarized as follows: Conforms to air-quality YES NO A 29 13 Supplier B 24 10 31 7 What is the probability of an emission conforms to air-quality and Supplied from B?