(5) Sally has caught COVID but doesn't know it yet. She is testing herself with rapidantigen kits which have an 80% probability of returning a positive result for an infectedperson. For the purpose of this question you can assume that the results of repeatedtests are independent.(a) If Sally uses 3 test kits what is the probability that at least one will return apositive result?(b) In 3 tests, what is the expected number of positive results?1(c) Sally has gotten her hands on more effective tests, these ones have a 90% prob-ability of returning a positive result for an infected person. If she tested herselftwice with the new tests, how many positive results would she expect to see?

Here given, Sally has caught COVID but doesn't know it yet. She is testing herself with rapid…

Answered: tests are independent. (a) If Sally…

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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In a remote jungle village the probability of a child contracting malaria is .45 the probability of contracting measles is.65 and the probability of contracting both is .20 What is the probability of a child contracting malaria or measles?
There was a baseball game between Oscar and Gabe. The chance of Oscar winning is 3/5 (60%). The chance of Gabe winning is 2/5 (40%). This game wasn't a one game competition. It's the best of 5 series. This means the first person to win 3 games is the overall champion. What's the probability (% is best) that Oscar is the champion? Don't answer this question as Oscar with a 60% chance and Gabe as a 40% chance. Also, don’t use the equation for finding multiple events for probability.
In a recent year, the Better Business Bureau settled 75% of complaints they received. You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Suppose your sample size is 288. What is the probability that the sample proportion will be at most 4 percent more than the population proportion?
Q. 2 A car dealer notes the following probabilities about his customers: P(those who buy a new car) = 0.25 P(those who buy a European car) = 0.30 P(those who neither buy a new car nor an European car) = 0.54 Find the probability that next customer buys a new European car?
If you play roulettes and bet on 'red' the probability that you win is 18/38 = .4737. People often repeat this between several times. We can consider each time we play a 'trial' and consider it a success when we win, so p = 18/38 or (.4737) and q = 20/38 or (.5263). Suppose that Caryl always places the same bet when she plays roulette, $5 on 'red'. Caryl might play just once, or might play several times. She has a profit (having won $5 more times than she lost $5) if she wins more than half of the games she plays. -when you play 401 times, p is the proportion of those 401 games that you win. You'll profit (winning more than you lose) if you win more than half of your bets p > .5000. c) what is the mean or expected value of p? d) what is the standard deviation of p? e) assume that the distribution of p is Normal and find the probability that Caryl will have a profit if she plays 401 times. show your work or calculator input and round your answer to four decimal places
A study tracked a large group of people for 10 years. At the start of the study, 20% were heavy smokers (H), 30% were light smokers (L), and 50% were non-smokers (N). The interest of the study was whether the people in the study died during the study (D) or not die (Dc ). The probability that a light smoker died during the study was twice that of the probability of a non-smoker dying. Also, the probability that light smoker died during the study was half that of the probability of a heavy smoker dying. A randomly selected person from the study died during the study. What is the probability that this person was a heavy smoker (given they died, what is the probability they were a heavy smoker H)?
Richard has just been given a 10-question multiple-choice quiz in his psychology class. Each question has five answers, of which only one is correct. Since he has not attended class recently, he doesn’t know any of the answers. What makes up a trial? What is a success? What is a failure? What are the values of n, p, and q? Assuming Richard guesses on all 10 questions, find the indicated probabilities. What is the probability that he will answer all 10 correctly. What is the probability that he will answer all 10 incorrectly. What is the probability that he will answer at least one of the questions correctly. What is the probability that he will get at most 3 correct? What is the average number(expected value) of questions Richard will answer correctly What is the standard deviation?
Q. 2 A car dealer notes the following probabilities about his customers: P(those who buy a new car ) = 0.25 P(those who buy a European car) = 0.30 P(those who neither buy a new car nor an European car ) = 0.58 Find the probability that next customer buys a new European car?
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) = 0.45 P(medium-quality oil) = 0.25 P(no oil) = 0.30 a. What is the probability of finding oil (to 2 decimals)? 0.70 b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below. P(soil high-quality oil) = 0.20 P(soil medium-quality oil) = 0.90 P(soil no oil) 0.20 Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals). P(high-quality oil soil) 0.2308 P(medium-quality oil soil) 0.5769 X P(no oil soil) 0.1538 What is the new probability of finding oil (to 4 decimals)? Medium-quality 0.8077 According to the revised probabilities, what is the quality of oil that is most likely to be found?
2. Wallace figures his chances of getting a new car for graduation at 70% if he graduates as class valedictorian. He only has about a 25% chance of getting a new car if he graduates 2nd or lower. He estimates his chances of being valedictorian at 50/50. What is the likelihood that Wallace will get a new car?
Thank you. I'm not sure about the result for the second question. What I'm having a hard time with is the probability that a total of 30 of the 546 crashes have occurred in the 48 time windows. My data shows that crashes occurred in 25 of these 48 time windows, with 3 in one of these and 2 in three others.
You are dealt a randomly chosen 5 card hand from a standard playing deck. The score S for a hand is 7 times the number of kings minus 2 times the number of clubs. What is the expected value of S?

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