O Examples of each display type with several conditional probability computations and explanations of how the computations are related to the display type Two-way table " Venn diagram Tree O Computations distinguishing between combinations and permutations " -

O Examples of each display type with several conditional probability computations and explanations of how the computations are related to the display type Two-way table " Venn diagram Tree O Computations distinguishing between combinations and permutations " -

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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which of the following are true about probabilities?
Obstetrics Suppose that infants are classified as low birthweight if they have a birthweight <2,500 g and as normal birthweight if they have a birthweight 22,500 g. Suppose that infants are also classified by length of gestation in the following five categories: <28 weeks, 28-31 weeks, 32-35 weeks, 36 weeks, and 237 weeks. Assume the probabilities of the different periods of gestation are as given in the table below. Length of gestation Probability <28 weeks 28-31 weeks 32-35 weeks 36 weeks 237 weeks 0.009 0.010 0.052 0.038 0.891 Also assume that the probability of low birthweight is 0.947 given a gestation of <28 weeks, 0.700 given a gestation of 28-31 weeks, 0.433 given a gestation of 32-35 weeks, 0.199 given a gestation of 36 weeks, and 0.030 given a gestation of 237 weeks. (a) What is the probability of having a low birthweight infant? (Round your answer to four decimal places.) (b) Show that the events (length of gestation ≤ 31 weeks) and (low birthweight} are not independent.…
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?
Find P(A or B or C) for the given probabilities. P(A) = 0.34, P(B) = 0.25, P(C) = 0.16 P(A and B) = 0.11, P(A and C) = 0.03, P(B and C) = 0.07 P(A and B and C) = 0.01 P(A or B or C) =
Events A and B are independent events with P(A) = 0.25 and P(B) = 0.35. The probability of the complement of Event B equals
Obstetrics Suppose that infants are classified as low birthweight if they have a birthweight <2,500 g and as normal birthweight if they have a birthweight 22,500 g. Suppose that infants are also classified by length of gestation in the following five categories: <28 weeks, 28-31 weeks, 32-35 weeks, 36 weeks, and 237 weeks. Assume the probabilities of the different periods of gestation are as given in the table below. Length of gestation <28 weeks Probability. 0.006 0.010 28-31 weeks 32-35 weeks 36 weeks 0.035 237 weeks 0.900 The following conditional probabilities are given: assume that the probability of low birthweight is 0.948 given a gestation of <28 weeks, 0.700 given a gestation of 28-31 weeks, 0.432 given a gestation of 32-35 weeks, 0.202 given a gestation of 36 weeks, and 0.028 given a gestation of 237 weeks. (a) What is the probability of having a low birthweight infant? (Round your answer to four decimal places. Hint: Use the Law of Total Probability.) 0.06612 0.049 (b) Show…
Indicate whether the statement is true or false, and justify your answer.All perceived probabilities are weighted lower than actual probabilities.
two way table Pathology Pediatrics Psychiatry Male 2950 1380 270 4600 Female 1550 1320 1530 4400 4500 2700 1800 9000 Find each of the following conditional probabilities a) Are the events E = 'Female' and F = 'Pathology' dependent or independent? Explain why. b) Are the events F = 'Male' and G = 'Pediatrics' dependent or independent? Explain why.
For each set of probabilities, determine whether the events A and B are independent or dependent. (If necessary, consult a list of formulas.) Probabilities Independent Dependent = P(A 18) - 1 (a) P(A)=-;P(B) =;P(A\B) = 5 1 1 P(A) =;P (B) = P(A and B) = %3D 4 6. 1 1 P (B|A) = 1 (c) P(4)-극: P(B)-P(Bl4): %3D %3D 1 1 (d) P(A) = : P(B) = P(4 |B) = | %3D
At the close of the stock markets on a day in 2013, there were 5905 companies listed with a certain stock exchange. On this day, the probabilities of advancing, declining, and unchanged company stocks appears in the table for the two exchanges. Find the probability an unchanged stock was listed on Exchange 1. Exchange Exchange 1 Exchange 2 Percentage of Probability of Probability of Stock Stock Companies Listed Advancing Declining 0.045 0.267 0.047 0.297 54.4% 45.6% The probability that an unchanged stock was listed on Exchange 1 is (Round to three decimal places as needed.) Probability the Stocks Remain Unchanged 0.045 0.047
After a workday, you visit a bar from monday to friday. The bar offers four differrent beer flavors. Each day you select one flavor with the following probabilities: flavor 1 with 30% flavor 2 with 25% flavor 3 with 40% flavor 4 with a 5% What is the probability that the first time you eat flavor 3 is on tuesday?
P(A)=0.55,P(B)=0.58,P(B∪A)=0.86 Find the following probabilities. P(A∩B) = P(B|A) = P(A|B) =