Homework Help is Here – Start Your Trial Now!
Math
Probability
It has recently been discovered that a small number of people have a genetic mutation that gives them latent superpowers, known as the sigma-gene. A laboratory test has been created to help identify people with the sigma- gene, which returns either "positive" (indicating the subject has the sigma-gene) or "negative" (indicating the subject does not have the sigma-gene). The test returns a "true positive" result for 95% of people who do in fact have the sigma-gene. However, the test also returns a "false positive" result for 10% of people who do not have the sigma-gene. Anyone who is suspected of having the sigma-gene must take the test exactly twice. (a) What is the probability that a person who has the sigma-gene receives at least one negative result out of their two tests? (b) Many people on the island of Genosha have taken the test twice. It is discovered that 6% of these people received a positive result for both tests. Based on this information, what proportion of people from the island actually have the sigma-gene? 因回 (c) Jayden lives on Genosha. They took the test twice and received different results. What is the probability that Jayden has the sigma-gene?

It has recently been discovered that a small number of people have a genetic mutation that gives them latent superpowers, known as the sigma-gene. A laboratory test has been created to help identify people with the sigma- gene, which returns either "positive" (indicating the subject has the sigma-gene) or "negative" (indicating the subject does not have the sigma-gene). The test returns a "true positive" result for 95% of people who do in fact have the sigma-gene. However, the test also returns a "false positive" result for 10% of people who do not have the sigma-gene. Anyone who is suspected of having the sigma-gene must take the test exactly twice. (a) What is the probability that a person who has the sigma-gene receives at least one negative result out of their two tests? (b) Many people on the island of Genosha have taken the test twice. It is discovered that 6% of these people received a positive result for both tests. Based on this information, what proportion of people from the island actually have the sigma-gene? 因回 (c) Jayden lives on Genosha. They took the test twice and received different results. What is the probability that Jayden has the sigma-gene?

A First Course in Probability (10th Edition)
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...
See similar textbooks
icon
Related questions
Topic Video
Question

R3

It has recently been discovered that a small number of people have a genetic mutation that gives them latent superpowers, known as the sigma-gene. A laboratory test has been created to help identify people with the sigma- gene, which returns either "positive" (indicating the subject has the sigma-gene) or "negative" (indicating the subject does not have the sigma-gene). The test returns a "true positive" result for 95% of people who do in fact have the sigma-gene. However, the test also returns a "false positive" result for 10% of people who do not have the sigma-gene. Anyone who is suspected of having the sigma-gene must take the test exactly twice. (a) What is the probability that a person who has the sigma-gene receives at least one negative result out of their two tests? (b) Many people on the island of Genosha have taken the test twice. It is discovered that 6% of these people received a positive result for both tests. Based on this information, what proportion of people from the island actually have the sigma-gene? (c) Jayden lives on Genosha. They took the test twice and received different results. What is the probability that Jayden has the sigma-gene?
Transcribed Image Text:It has recently been discovered that a small number of people have a genetic mutation that gives them latent superpowers, known as the sigma-gene. A laboratory test has been created to help identify people with the sigma- gene, which returns either "positive" (indicating the subject has the sigma-gene) or "negative" (indicating the subject does not have the sigma-gene). The test returns a "true positive" result for 95% of people who do in fact have the sigma-gene. However, the test also returns a "false positive" result for 10% of people who do not have the sigma-gene. Anyone who is suspected of having the sigma-gene must take the test exactly twice. (a) What is the probability that a person who has the sigma-gene receives at least one negative result out of their two tests? (b) Many people on the island of Genosha have taken the test twice. It is discovered that 6% of these people received a positive result for both tests. Based on this information, what proportion of people from the island actually have the sigma-gene? (c) Jayden lives on Genosha. They took the test twice and received different results. What is the probability that Jayden has the sigma-gene?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Algebraic Operations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS