**Understanding False-Positive Rates in Polygraph Tests**A false-positive in a polygraph test occurs when an individual who is telling the truth fails the lying-detector test. The probability of this happening is 15%. To delve into this concept, let's consider an experiment where we administer a polygraph test to a group of randomly selected individuals and record the occurrence of false-positives.**Questions to Explore:**1. **Probability of First False-Positive with Third Person Tested:** - What is the probability that the first false-positive will occur when the third person is tested?2. **Probability of Fewer than 4 People Tested Before First False-Positive:** - What is the probability that fewer than 4 people are tested before the first false-positive occurs?3. **Probability of More than 3 People Tested Before First False-Positive:** - What is the probability that more than 3 people are tested before the first false-positive occurs?4. **Expected Value of False-Positives:** - What is the expected value of false-positives?5. **Variance in the Experiment:** - What is the variance in this experiment?These questions can help us understand the statistical properties of polygraph test results and assess the reliability and variation in outcomes. By answering these, we can better comprehend the effectiveness and challenges associated with polygraph tests in practical scenarios.---*Note: For detailed understanding, one might need to refer to concepts from probability theory and statistics, specifically those dealing with geometric distributions and expected values.*

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A false-positive in a polygraph test, that is, an individual who fails a lying-detector test even though they are telling the truth, has a probability of 15 %. Consider the experiment of administering a lie-detector or polygraph test (these are synonyms or words that have the same meaning in common usage) to a group of randomly selected people and recording false-positives. i) What is the probability that the first false-positive will occur when the third person is tested? ii) What is the probability that fewer than 4 people are tested before the first false-positive occurs? iii) What is the probability that more than 3 people are tested before the first false-positive occurs? iv) What is the expected value of false-positives? v) What is the variance in this experiment?

A false-positive in a polygraph test, that is, an individual who fails a lying-detector test even though they are telling the truth, has a probability of 15 %. Consider the experiment of administering a lie-detector or polygraph test (these are synonyms or words that have the same meaning in common usage) to a group of randomly selected people and recording false-positives. i) What is the probability that the first false-positive will occur when the third person is tested? ii) What is the probability that fewer than 4 people are tested before the first false-positive occurs? iii) What is the probability that more than 3 people are tested before the first false-positive occurs? iv) What is the expected value of false-positives? v) What is the variance in this experiment?

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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