a) A study has determined that the occupation of a boy as an adult, depends uponthe occupation of his father and is given by the following transition matrix, whereP = professional, F = farmer, and L = laborerFather's occupationP FP [0.80.30.2]Son'sF0.10.50.2оссираtionL 0.10.20.6Thus the probability that son of a professional will also be a professional is 0.8 andso on.i)What is probability that the grandchild of a professional will be a farmer?ii)In the long run, what proportions of the population will be former?

Answered: Image /qna-images/answer/6f1efcbf-e054-4c9a-a80f-ed3d0627c5b0.jpg

Answered: a) A study has determined that the…

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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There are three kinds of vegetation in an ecosystem: grass (G), shrubs (S), and trees (T) (Bodine, Lenhart, and Gross 2014). Every year, 25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of trees are converted to shrubs, and 1% of trees are converted to grass; the other transition probabilities are 0. Calculate the probability of a plot of land have the following succession of vegetation from year to year: GSGG, taking the first state as given. (type three digits after the decimal).
The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. 0.4 2300 T 0.3 2800 0.2 2500 2400 From/To A B C D A 0.2 0 0.3 0.3 B 0.3 0.2 0.5 0.4 C 0.1 0.5 0 0.3 D 0 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. c) What is the mean return time of Brand A? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? Number of Customers d) What is the percentage change of Brand B? Answer in percentage and in 2 decimal places.
A cigarette company wants to promoe thne sales of X's cigarettes (Brand) with special advertising campaign. Fifty out of every thousand cigarettes are rolled up in gold foil and randomly mixed with the regular (special king-sized, mentholated) cigarettes. The company offers to trade a new package of cigarettes for each gold cigarette a smoker finds in a package of Brand X. What is the probability that buyers of Brand X will find X = 0, 1, 2, 3, . gold cigarettes in a single package of 10 ? ...
A blood bank asserts that a person with type O blood and a negative Rh factor (Rh−) can donate blood to any person with any blood type. Their data show that 49% of people have type O blood and 17% of people have Rh− factor; 52% of people have type O or Rh− factor. A. Find the probability that a person has both type O blood and the Rh− factor. B. Find the probability that a person does NOT have both type O blood and the Rh− factor.
Consider an M/M/1 queueing system. Find the probability of finding at least n customers in the system.
All human blood can be "ABO-typed" as one of O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen person in a country. Blood type A National probability 0.43 0.12 AB ? (a) What is the national probability of type AB blood? O 0.41 (b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly chosen person from this country can donate blood to Maria?
The genotype of an organism can be either normal (wild type, W) or mutant (M). Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring.
A company buys microchips from three suppliers I, II and III. Supplier I has a record of providing microchips that contain 10% defective; supplier a defective rate of 5% and supplier III has a defective rate of 3%. Suppose 10%, 40% and 50% of the current supply came from suppliers I, II and III, respectively. If a randomly selected microchip is defective, what is the probability that it came from supplier II? Express your answer accurate to two decimal places. O 48 O..40 O something else O 44 O 41
Super D is a major video distributor that purchases blank SD Drives from two sources: Disk Makers, which provides 73% of the SD Drives, and Media Supply, which provides the remaining 27% . Historically,4% of the SD Drives Super D has purchased from Disk Makers have been defective, whereas 8% of the SD Drives purchased from Media Supply have been defective. A randomly selected SD Drive is found to be defective. Use Bayes' Theorem to determine the probability that the SD Drive came from Disk Makers.
The circuit shown below operates if and only if there is some path of functional devices from left to right. The probability that each device functions is shown for each device and the devices operate independently of each other. What is the probability that the circuit operates? 0.9 0.9 0.8 0.95 0.95 0.9 (A) None of these (B) 0.5263 (C) 0.1642 (D) 0.9850 (E) 0.9702
An insurance company calculates car insurance company calculates car insurance premiums based on the age of the policyholder according to three age groups: Group A consists of drivers younger than 22 years old; Group B consists of drivers 22—33 years old, and Group C consists of drivers older than 33 years.Its portfolio consists of 10% Group A policyholders, 38% Group B policyholders and 52% Group C policyholders. The probability of a claim in any 12 month period for a policy belonging to Group A, B or C is 13%, 3% and 2%, respectively. (i) Calculate the probability that a randomly chosen policy holder from this portfolio will make a claim during a 12 month period. One of the company’s policyholders has just made a claim(ii) Calculate the probability that the policy holder is younger than 22 years.
A social event allows free entrance to those with Aim High credit card or those with the car Elite. The probabilities of having Aim High and Elite among the employees of a company are 0.10 and 0.05, respectively. Having Aim High is found to be independent of owning Elite. If 1,000 invitations are sent randomly to employees of the company, estimate the number who will be given free entrance.

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