Visitors to your website are asked to answer a single “yes or no” survey question before they get access to the content on the page. Among all of the visitors to this page, there are two categories: Random Clicker (RC) and Truthful Clicker (TC). There are two possible answers to the survey: yes and no. Random clickers would click either one with equal probability. You are also given the information that the overall fraction of random clickers is 0.3. After a trial period, you get the following survey results: 65% said Yes and 35% said No. What is your estimate for P(yes | TC), the probability that someone answers “yes” to the survey question, given that they were a truthful clicker? Hint: use the rule of total probability

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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Visitors to your website are asked to answer a single “yes or no” survey question before they get access to the content on the page. Among all of the visitors to this page, there are two categories: Random Clicker (RC) and Truthful Clicker (TC). There are two possible answers to the survey: yes and no. Random clickers would click either one with equal probability. You are also given the information that the overall fraction of random clickers is 0.3. After a trial period, you get the following survey results: 65% said Yes and 35% said No. What is your estimate for P(yes | TC), the probability that someone answers “yes” to the survey question, given that they were a truthful clicker? Hint: use the rule of total probability

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