Let denote the probability that a randomly sampled individual in some population votedConservative in the last General Election. In a particular type of 'randomised response'experiment, each of a random sample of individuals from this population responds 'True' or'False' to one of the following two statements.(a) I voted Conservative at the last General Election.(b) I did not vote Conservative at the last General Election.A randomising device is used to ensure that the probabilities of responding to (a) and (b) are pand 1-p respectively, where p is known and 0

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Answered: Let 0 denote the probability that a…

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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A test to determine whether a certain antibody is present is 99.4% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.4% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.006. Suppose the test is given to seven randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all seven people? (b) What is the probability that the test comes back positive for at least one of the seven people?
A test to determine whether a certain antibody is present is 99.7% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.7% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.003. Suppose the test is given to seven randomly selected people who do not have the antibody. What is the probability that the test comes back negative for all sevenpeople? and what is the probability that the test comes back positive for at least one of the seven people?
A test to determine whether a certain antibody is present is 99.2% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.2% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.008. Suppose the test is given to six randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all six people? (b) What is the probability that the test comes back positive for at least one of the six people?
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?
A marketing firm would like to test-market the name of a new energy drink targeted at 18- to 29-year-olds via social media. Suppose a study found that 36% of adults (18 and older) do not use social media. Suppose the percentage of adults age 30 and older is 75%. Suppose that the percentage of the adult population that is either age 18-29 or uses social media is 64%. What is the probability that a randomly selected adult is 18-29 and a user of social media? Your answer should be expressed as a number between 0 and 1, and it has to contain 2 decimal places.
Let the random variable X denote the number of girls in a five-child family. If the probability of a female birth is 0.5, find the following probabilities. (a) Find the probability of 0, 1, 2, 3, 4, and 5 girls in a five-child family. (Round your answers to three decimal places.) P(0 girls) = P(1 girl) = P(2 girls) = P(3 girls) = P(4 girls) = P(5 girls) = (c) Compute the mean and the standard deviation of the random variable X. (Round your standard deviation to three decimal places.) mean __ girls standard deviation __ girls
A study reported that about 40% of high school students have tried out for a sport at their school. To find out if this applies to Jessica’s school, she surveyed an SRS of 20 students. Nine of them said that they had tried out for a sport. To see if this result is surprising, a simulation is to be conducted to estimate the probability of obtaining a sample result as high as this one. Let 0–3 represent students who tried out for a sport and 4–9 represent students who did not try out for a sport. Using the line of random numbers to run one simulation, what proportion of students tried out for a sport? 0.40 0.45 0.50 0.60
The accompanying data are from an article. Each of 309 people who purchased a Honda Civic was classified according to gender and whether the car purchased had a hybrid engine or not. Male Female Hybrid 76 33 Not Hybrid 116 84 Suppose one of these 309 individuals is to be selected at random. Determine if the probabilities P(hybrid male) and P(male hybrid) are equal. If not, explain the difference between these two probabilities. O Yes, the probabilities are equal. No, the probabilities are not equal. The first is the probability that a hybrid Honda Civic owner is male, and the second is the probability that a male Honda Civic owner purchased a hybrid. O No, the probabilities are not equal. The first is the probability that a male Honda Civic owner purchased a hybrid, and the second is the probability that a hybrid Honda Civic owner is male.
A pharmaceutical company is running trials on a new test for anabolic steroids. The company uses the test on 400 athletes known to be using steroids and 200 athletes known not to be using steroids. Of those using steroids, the new test is positive for 375 and negative for 25. Of those not using steroids, the test is positive for 25 and negative for 175. What is the relative frequency of a false negative result (the probability that an athlete using steroids will test negative)? (Round your answer to two decimal places.) What is the relative frequency of a false positive result (the probability that an athlete not using steroids will test positive)? (Round your answer to two decimal places.)
A test to determine whether a certain antibody is present is 99.6% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.6% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.004. Suppose the test is given to four randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all four people? (b) What is the probability that the test comes back positive for at least one of the four people? (a) P(all 4 tests are negative) = (Round to four decimal places as needed.) (b) P(at least one positive) = (Round to four decimal places as needed.)
In an inspection of automobiles in a certain Country, 60% of all automobiles had emissions that did not meet EPA regulations. For a random sample of 10 automobiles, compute the following probabilities: a. All 10 automobiles failed the inspection. b. Exactly 6 of the 10 failed the inspection. c. Six or more failed the inspection. d. All 10 passed the inspection.

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