A diagnostic test is a procedure which gives a quick, but not always reliable, indication of whether a patient has a certain disease. Test results are said to be "positive" if, after testing, the person is thought to have the disease and "negative" if the personis thought not to have the disease.In a particular region, 3% of the population is thought to have a certain disease. A standard diagnostic test has been found to correctly identify 93% of the people who have the disease. However, the test also incorrectly diagnoses 7% of those who do nothave the disease as having the disease (in other words, the person does not have the disease but the test tells them that they do).A randomly selected person in the region is tested for the disease.(a) What is the probability the test comes back positive?(b) What is the probability the test comes back positive and the person actually has the disease?(c) If the test comes back positive, what then is the conditional probability that the person actually does have the disease?

Name: A diagnostic test is a procedure which gives a quick, but not always
Uploaded: 2024-03-20T07:07:00.000Z
Channel: Bartleby
Description: A diagnostic test is a procedure which gives a quick, but not always reliable, indication of whether a patient has a certain disease. Test results are said to be "positive" if, after testing, the person is thought to have the disease and "negative"

The formula for computing the probability that the test is positive is, P( test is positive) = {P(…

Math

Probability

a particular region, 3% of the population is thought to have a certain disease. A standard diagnostic test has been found to correctly identify 93% of the ve the disease as having the disease (in other words, the person does not have the disease but the test tells them that they do). andomly selected person in the region is tested for the disease. (a) What is the probaility the test comes back positive? (b) What is the probability the test comes back positive and the person actually has the disease?

a particular region, 3% of the population is thought to have a certain disease. A standard diagnostic test has been found to correctly identify 93% of the ve the disease as having the disease (in other words, the person does not have the disease but the test tells them that they do). andomly selected person in the region is tested for the disease. (a) What is the probaility the test comes back positive? (b) What is the probability the test comes back positive and the person actually has the disease?

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

Related questions

Q: A survey conducted on a randomly selected day for an ice cream truck showed that 68% of customers…

A: The conditional probability is computed as PAB=PA∩BPB

Q: A veterinarian has invented an allergy test for cats. Sam the cat seems to be allergic to tina the…

A: Probability of being allergic = 2%=0.02 Given that the test correctly indicates an allergy 98%=0.98…

Q: A survey showed that 72% of adults need correction (eyeglasses, contacts, surgery etc) for their…

Q: 3 students are choosing between loose leaf, hardback and electronic texts. Studies have show that…

Q: 3) In the United States, 56% of all children get an allowance and 40% of all children get an…

A: Let H -do household chores Let A -Child gets an allowance P(A) = 0.56 and P(A and H) = 0.40

Q: If team B is the underdog in playing team C and has probability 1/4 of winning every game it plays…

A: The probability of team B winning the game is, P(B)=14The probability that team C wins every game it…

Q: Freezy’s Ice Cream Stand is testing out new flavors, Pumpkin Spice and Cotton Candy. A poll…

A: A poll conducted by Freeze's showed that A = 30 customers liked Pumpkin Spice B = 55 customers liked…

Q: The probability of winning the grand prize at a particular carnival game is 0.008. Michele wins the…

A: From given data the probability 0f winning the grand prize at a particular carnival game is 0.008

Q: A research team conducted a study showing 25% of business men who wear ties wear them too tight. At…

A: Obtain the probability that at least one tie is too tight. The probability that at least one tie is…

Q: 30% of bacteria (B) strains are resistant to antibiotic (A). Bacteria from 7 individuals was…

Q: Based on long experience, an airline found that about 4% of the people making reservations on a…

A: a. It is given that 4% of the people making a reservation do not show up. This indicates that the…

Q: A survey of athletes at a high school is conducted, and the following facts are discovered: 28% of…

A: Let F - football players B - basketball players. P(F) = 0.28 P(B) = 0.71 P(F and B) = 0.03

Q: February 2U, 2022 at 5-06 PM Hannah is an obstetrician with 13 diabetic patients. The probability…

Q: 5. A parent takes a child to the county fair. There is an exhibit where you can win a stuffed animal…

Q: 2. You are invited to play a game in which you roll two fair dice. If you roll a 7, you eds- in…

Q: 3 students are choosing between loose leaf, hardback and electronic texts. Studies have show that…

Q: If 42% of students own a car and 27% of students own a bike. What is the probability that a student…

A: Given Data: The probability that student own a car is: P(A)=42% The probability that student own a…

Q: English and American spellings are rigour and rigor respectively. A man staying at a Parisian hotel…

A: Let A=writer is an AmericanE=writer is English manV=a letter found to be a vowelP(A)=0.6P(E)=0.4

Q: Joe is playing an arcade game and has 8 chances to knock down the moving ducks. A person playing…

A: 1.Find the probability that Joe hits the fourth duck:A person playing the Arcade game hits the…

Q: Leghorn chickens are raised for laying eggs. Suppose the probability of a female chick hatching from…

A: (a)Let us define the random variable X as the number of female chicks and follows Binomial…

Q: 12% of baseball players tested positive for drugs at some point this season. Of these players, 5%…

A: Let P1=Instance that player was tested positive this season. P2=Instance that player was tested…

Q: Suppose a flu test has the following results: If a person is healthy, it returns negative 90% of…

A: Given Information: If a person is healthy, it returns negative 90% of the timeIf a person is…

Q: what is the probability of landing in a circle on the ground between 2 and 4 times including 2 and…

A: Here given suppose there is a game where you throw a marble and, if it lands in a circle on the…

Q: Suppose a there is a 40% chance a randomly selected person likes strawberry ice cream, a 70% chance…

A: (1) Obtain the probability that a randomly selected person likes chocolate ice cream but not…

Q: A survey of athletes at a high school is conducted, and the following facts are discovered: 33% of…

A: Let A be the event of playing football B be the event of playing basketball Given data,…

Q: A fair 2-sided coin is tossed 3 times. What is the probability that the coin lands on tails once?

A: A fair 2- sided coin is tossed 3 times. then sample space(S); S={HHH,HHT,HTH,THH,TTH,THT,HTT,TTT}…

Q: Composite blood testing is sometimes used to save costs. A Hepatitis-C composite blood test means…

Q: In a city, assume 25% of citizens are smokers. When 20 people in the city are randomly surveyed,…

A: Solution: a. Let X be the number of people are smokers and n be the sample number of people. From…

Concept explainers

2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

Topic Video

Question

100%

A diagnostic test is a procedure which gives a quick, but not always reliable, indication of whether a patient has a certain disease. Test results are said to be "positive" if, after testing, the person is thought to have the disease and "negative" if the person
is thought not to have the disease.
In a particular region, 3% of the population is thought to have a certain disease. A standard diagnostic test has been found to correctly identify 93% of the people who have the disease. However, the test also incorrectly diagnoses 7% of those who do not
have the disease as having the disease (in other words, the person does not have the disease but the test tells them that they do).
A randomly selected person in the region is tested for the disease.
(a) What is the probability the test comes back positive?
(b) What is the probability the test comes back positive and the person actually has the disease?
(c) If the test comes back positive, what then is the conditional probability that the person actually does have the disease?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Proportions$

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.

Similar questions

A survey of athletes at a high school is conducted, and the following facts are discovered: 28% of the athletes are football players, 69% are basketball players, and 14% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player?Probability = % (Please enter your answer as a percent)
Is the event independent or dependent and what is the probability of the event? Drawing three queens in a row from a standard deck of cards when the drawn card is returned to the deck each time.
The probability that a statistics graduate from a Canadian university gets a data science job is 0.6. Ten graduates applied for executive jobs. (a) What is the probability that exactly 3 will get jobs? (b) What is the probability that at least 2 will get a job?
A common practice of airline companies is to sell more tickets for a particular flight than there are seats on the plane, because customers who buy tickets do not always show up for the flight. Suppose that the percentage of no-shows at flight time is 2%. For a particular flight with 246 seats, a total of 250 tickets were sold. What is the probability that the airline overbooked this flight?
A survey of athletes at a high school is conducted, and the following facts are discovered: 39% of the athletes are football players, 36% are basketball players, and 24% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player?Probability = % (Please enter your answer as a percent)
A survey of athletes at a high school is conducted, and the following facts are discovered: 19% of the athletes are football players, 28% are basketball players, and 2% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that he is either a football player or a basketball player? Probability = % (Please enter your answer as a percentage)
The recent storm, Maring, caused a lot of people to get infected with a disease. Doctors estimate that a person who got infected with the disease can recover with a probability of 40%. If 15 people from a certain barangay in QC are known to have been infected with the disease, what is the probability that from 3 to 8 survive?
A of athletes at a high school is conducted, and the following facts are discovered: 25% of the athletes are survey football players, 60% are basketball players, and 13% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player? Probability = (Please enter your answer as a percent) License
(b)What is the probability that more than 7 have hypertension? The probability that more than 7 have hypertension is?
The mayor conducted a survey of 1000 residents, where 486 are in favor of proposal 1, 372 in favor of proposal 2, and 134 in favor of both proposal 1 and 2. What's the probability that a resident isn't in favor of either proposal 1 or 2?
Cheetahs account for 44% of big cats in zoos, with males accounting for 25%. . Also, 68% of the males are cheetah. A large cat is chosen at random. What is the probability that it is a male cheetah?
A group of students and faculty of UO are polled about whether or not UO should switch to a 4 day work week. The results are attached in the screen shot. What are the probability of a student voting "in favour"?