Samples of skin experiencing desquamation are analyzed for both moisture and melanin content.The results from 100 skin samples are as follows:Melanin ContentHighLowMoisture High137ContentLow4832Let A denote the event that a sample has high Melanin Content, and let B denote the event that asample has low Moisture Content. Determine the following probabilities: P(A|B) and P(B|A).(Show complete solution in your answer sheet)a. 0.35, 0.1795b. None among the choicesc. 0.60, 079d. 0.1795, 0.35

Conditional probability is the Probability of one event occurs, given that another event will occur.…

Answered: Samples of skin experiencing…

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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You are enrolled in MBA 440. At the beginning of the semester, you used your hunch to estimate the likelihood of passing this class. Let P be the event of passing the class; F is the event of failing the class. Your prior probabilities are as follows: P(P)=0.7 P(F)=0.3 After the first week of class, you find out that you have failed the first assignment. Let A1 be the event of passing the first assignment; let A2 be the event of failing the first assignment. Now you feel you need to update your belief about the likelihood of passing this class. You talk to your Professor and she tells you that given someone has passed the class, the probability of passing the first assignment is 0.8, i.e. P(A1|P)=0.8. She also gives you the following conditional probabilities: P(A2|P)=0.2; P(A1|F)=0.3 and P(A2|F)=0.7. What is the posterior probability that you will pass this class given that you have failed the first assignment?
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A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.95, P(C) = 0.91, and P(D) = 0.96. Find the probability that at least one of the four parts will work. Round to six decimal places.
Let S be the educational attainment of individuals in a town, with values S-0 for less than high school and S=1 for high school or above. Also, let Y be their individual annual income with values Y-O for less than $20,000, Y-1 for between $20,000 and $40,000, and Y=2 for above $40,000. Consider now the following joint probabilities: Y-0 (less than $20K) Y-1 ($20K-$40K) Y-2 (more than $40K) 0.03 0.01 0.36 0.33 SIY S-0 (Less than HS) 0.05 Y-1 (HS or more) 0.22 Determine the conditional standard deviation of the level of educational attainment given that the individual annual income is between $20,000 and $40,000.
At the beginning of each day, a patient in the hospital is classifed into one of the three conditions: good, fair or critical. At the beginning of the next day, the patient will either still be in the hospital and be in good, fair or critical condition or will be discharged in one of three conditions: improved, unimproved, or dead. The transistion probabilities for this situation are Good Fair Critical Good 0.65 0.20 0.05 Fair 0.50 0.30 0.12 Critical 0.51 0.25 0.20 Improved Unimproved Dead Good 0.06 0.03 0.01 Fair 0.03 0.02 0.03 Critical 0.01 0.01 0.02 For example a patient who begins the day in fair condition has a 12% chance of being in critical condition the next day and a 3%…
A gas station has three grades of fuel, regular, premium and diesel. Due to problems with the supply chain, the probabilities that the station will run out of any three fuel types in a week are 0.10, 0.16 and 0.24, respectively. These probabilities are statistically independent. Also, if there is a shortage of diesel, the probability of a shortage of premium becomes 0.25. 1. How likely is the station to run out of all three fuels in a given week? 2. What is the probability that if regular runs out, both premium and diesel will also run out? 3. What is the probability that the station will run out of at least one of either premium and diesel? 4. What is the probability that the station will run out of at least 2 of the fuels in a week?
The accidents that occur in a manufacturing company were classified by severity (strong, moderate and mild) and by sex with the following characteristics: 40% of the accidents were strong and 30% were moderate. Women suffered 20% of the accidents. Of the total number of serious accidents, men suffered 85.5% of the accidents. Similarly, of the total moderate accidents, women suffered 45% of the accidents. Calculate the following probabilities:- If a woman suffered an accident, what is the probability that it was minor?- If a man suffered an accident, what is the probability that he is strong?
During the 1971-72 season, the Los Angeles Lakers won 69 games and lost 13. Assuming that the outcomes of the basketball games are independent and that the percentageof wins this season will be the same as in 1971-1972, answer the following questions: (a) What is the probability that the Lakers will win the first twogames of the season? (b) What is the probability that the Lakers will win the first sevengames of the season?

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