**Problem Statement:**Suppose you are a judge hearing a criminal appeal. Before looking into the facts of the case, you would like to get a sense of how likely it is that a given defendant was wrongfully convicted at trial. You know that trial juries are not perfect. They only convict guilty defendants 90% of the time, and wrongly convict innocent defendants 10% of the time. You also assess that 75% of the defendants who are brought to trial are actually guilty of their crimes. Using Bayes’ rule, determine the probability that a particular defendant is really innocent, given that he or she was convicted by a jury.

Answered: case, you would like to get a sense of…

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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Blood pressure: High blood pressure has been identified as a risk factor for heart attacks and strokes. The proportion of U.S. adults with high blood pr 0.4. A sample of 39 U.S. adults is chosen. Use the TI-84 Plus Calculator as needed. Round the answer to at least four decimal places. Part 1 of 6 Is it appropriate to use the normal approximation to find the probability that more than 43% of the people in the sample have high blood pressure? It is appropriate to use the normal curve, since np 15.6 |2 10 and n (1 – p) = 23.4 10. Part 2 of 6 Find the probability that more than 43% of the people in this sample have high blood pressure. The probability that more than 43% of the people in this sample have high blood pressure is .3511 AI
85% of the restaurants in Camden Town practice good hygiene. Each time you eat in a clean restaurant, there is a 4% chance that you will get sick, independent of your previous visits. Each time you eat in a restaurant that does not practice good hygiene, on the other hand, there is a 40% chance that you will get sick, independent of your previous visits. 1. You eat at a restaurant in Camden Town and you get sick. What is the probability that the restaurant practices good hygiene? Hint: Using the law of total probability, first calculate the probability of the event ‘falling sick’. You can use this probability in your subsequent application of Bayes’ Theorem. 2. You go to the same restaurant for a second time, and you get sick again. What is the probability of the restaurant practicing good hygiene now? Hint: Using the law of total probability, first calculate the probability of the event ‘falling sick twice’. In this calculation, you can use the conditional independences P(falling sick…
Answer the Following Question Lavelle wears socks that are either red, white, or black. If there's a 28% chance that he'll wear white socks on a given day and a 42% chance of black socks, what is the probability of wearing red socks?
Can you please help me solve the question attached as an image?
We're thinking about children again - let's stick with our assumption that babies are boys with probability 0.51, girls with probability 0.49, and births are independent. You're a researcher interested in large families: as part of your latest project, you've decided to interview 50 families in which there are exactly eight children. The graph below illustrates the possible outcomes for a single family. What's the probability that you find one or more families in which the children are all of the same gender (i.e. all boys or all girls)? probability 0.3- 0.2 0.1- 0.0- 0 1 2 3 4 5 6 7 8 number of girls
Consider three classes (I, II and III) consisting of 30, 25, and 45 students. Suppose a student is selected from class I, then he has 10% chance to make an A. Assume that these probabilities for the class II and III are 15% and 20% respectively. If a student is selected randomly and has an A, what is the probability that he is from class II. Enter your answer to the nearest FOUR decimal places.
An organization conducts an annual survey of cybersecurity at firms from around the world. In a recent year, the organization sent survey questionnaires via email to all professionals that hold a certified information security manager designation. Of the 1,401 firms that responded to the survey, 1,107 (or 79 %) expect to experience a cyberattack (for example, aMalware, hacking, or phishing attack) during the year. You are to estimate the probability of an expected cyberattack at a firm during the year with a 95% confidence interval. Answer the followings: a. b. C. d. What is/are the critical value(s)? What is the margin of error? Identify the 95% confidence interval for the probability of an expected cyberattack at a firm during the year. If the margin of error should be 0.02 or less, what would be the minimum sample size?
Lando works in Brooklyn and his home is in Newark. He comes to office either by bus or train. If he arrives at office on time or earlier, 90% of the times he comes by train and if he is late, 70% of the times she comes by bus. Lando normally arrives at office on time for 80% of the times. What is the probability that he takes bus normally?
The management of marks department store estimates that approximately 6% of all shoppers shoplift. Of those people who shoplift, 98% are stopped by security. Of the other 94% of the shoppers, 1% are mistakenly identified as shoplifters by security. If a shopper is detained by security, what is the probability that the person was in fact a shoplifter?
The nursing department of a college surveyed two hundred graduates from their programs about their current work. The college has different levels of degrees in nursing available. The department found the following probabilities: P(bachelor's degree)= 0.45 P(working in nursing)=0.85 P(in nursing in bachelor's)=0.4 Find the probability that a graduate is currently working in nursing, given that they earned a bachelor's degree.
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In a certain school, 17% of the students are enrolled in a psychology course and 28% are enrolled in a foreign language course. Of those enrolled in a psychology course, 32% are enrolled foreign language course. What is the probability of a student enrolling in both a foreign language course and a psychology course?

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