6. A large group of people is to be checked for two common symptoms of a certain disease. It is thoughtthat 20% of the people possess symptom A alone, 30% possess symptom B alone, 10% possess bothsymptoms, and the remainder have neither symptoms. For one person chosen at random from thisgroup, find these probabilities(a) The person has neither symptom.(b) The person has at least one symptom.(c) The person has both symptoms, given that the person has symptom B.

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Answered: 6. A large group of people is to be…

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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5. Suppose that in a small city, 30% of the men smoke, while only 20% of the women smoke. You select six people at random (a mix of men and women), and want to find the probability that at least three of them smoke. Why is this not a binomial experiment? There are more than two possible outcomes for each trial. The trials are not independent of each other. The probability of “success” is not the same for each trial. There are not a fixed number of trials.
Question No.2- Suppose 200 men and 200 women participated in the study, and 280 reported they preferred plain bottled water. Of the group preferring a sports drink, 80 were men and 40 were women. a. What is the probability a person in the study preferred plain bottled water? b. What is the probability a person in the study preferred a sports drink? c. What are the conditional probabilities of woman given preferred plain water? e. Given a consumer is a man, what is the probability he will prefer a sports drink?
A certain undergraduate university consists of 35% freshmen, 28% sophomores, 25% Juniors, and the rest seniors. You learn that the probability a freshman will drop out during the current year is .12, the probability a sophomore will drop out during the current year is .08, and the probability a junior will drop out during the current year is .06. For some reason the drop-out rate for seniors was not reported. However, you learn that the dropout probability for all undergraduates is .088.What is the probability that a senior will drop out during the current year?
3.
7. There are 2,000 cars in City HK, which is divided into Zones A, B, C, and D. For any particular car, the probabilities of being in each zone are given by P(Zone A) = 0.3 P(Zone B) = 0.2 P(Zone C) 0.1 P(Zone D) 0.4.
40% of the people staying in a hotel business have breakfast at the hotel. 30 of them have dinner at the hotel. 20 of them eat breakfast and dinner at the hotel. The hotel would like to choose a random tourist from among the guests and reward them by paying all their expenses. Since it is known that the person to be rewarded is a tourist who has breakfast at the hotel, what is the probability of being a tourist who also eats dinner at the hotel?
Suppose that Art can decide to go to work by one of three modes of transportation, car, bus, or commuter train. Because of high traffic, if he decides to go by car, there is a 50% chance he will be late. If he goes by bus, which has special reserved lanes but is sometimes overcrowded, the probability of being late is only 20%. The commuter train is almost never late, with a probability of only 5%, but is more expensive than the bus. Suppose that Art is late one day, and his boss wishes to estimate the probability that he drove to work that day by car. Since he does not know which mode of transportation Art usually uses, he gives a prior probability of 1/3 to each of the three possibilities. What is the boss’ estimate of the probability that Art drove to work? Suppose that a coworker of Art’s knows that he almost always takes the commuter train to work, never takes the bus, but sometimes, 10% of the time takes the car. What is the co-workers probability that Art drove to work that day,…
I would like some help with this problem in the picture
A manufacturing plant produces light bulbs in three different colors: red, blue, and green. The probabilities of producing a red, blue, or green bulb are 0.2, 0.5, and 0.3, respectively. If a customer buys six bulbs at random, what is the probability of receiving at least two bulbs of each color?
20. Based on student records, 25% of the students at a large high school have a GPA of 3.5 or better, 16% of the students are currently enrolled in at least one AP class, and 12% of the students have a GPA of 3.5 or better and are enrolled in at least one AP class. If we select one student at random, what is the probability that the student has a GPA lower than 3.5 and is not taking any AP classes? (A) 0.29 (B) 0.47 (C) 0.53 (D) 0.63 (E) 0.71
Consider two events following receiving a bachelor’s degree from a prestigious university: A = {being accepted into a graduate program} and B = {receiving a job offer}. We know the following is true: P(A) = P(B) = 0.7 P(A|B) = 0.9 Are events A and B independent? Why or why not?
Hamza comes to office located in Islamabad through different modes of transport. From his past data, it is known that the probability of him coming through car, bus, motorbike and rickshaw are respectively 31 1 ,2 10'5'10 1 1 ,and -and- 5 The probabilities that he will arrive to his office late are if he comes by car, bus and motorbike. Interestingly, he will not be late if he comes by rickshaw. Suppose, he arrives late on Friday. What is the probability that he came by car?

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