Suppose two doctors, A and B, test all patients coming into a clinic for syphilis. Let events A+ = {doctor A makes a positive diagnosis} and B+ = {doctor B makes a positive diagnosis}. Doctor A diagnoses 25% of all patients as positive, doctor B diagnoses 40% of all patients as positive, and both doctors diagnose 10% of all patients as positive. 2.1 Are the diagnoses of the two doctors independent? 2.2 Suppose a patient is referred for further lab tests if either doctor A or B makes a positive diagnosis. What is the probability that a patient will be referred for further lab tests? 2.3 For a single patient, what is the probability of getting only one positive diagnosis from the two doctors?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Topic Video
Question

Suppose two doctors, A and B, test all patients coming into a clinic for syphilis.
Let events A+ = {doctor A makes a positive diagnosis} and B+ = {doctor B makes
a positive diagnosis}. Doctor A diagnoses 25% of all patients as positive, doctor B
diagnoses 40% of all patients as positive, and both doctors diagnose 10% of all
patients as positive.
2.1 Are the diagnoses of the two doctors independent?
2.2 Suppose a patient is referred for further lab tests if either doctor A or B
makes a positive diagnosis. What is the probability that a patient will be referred
for further lab tests?
2.3 For a single patient, what is the probability of getting only one positive
diagnosis from the two doctors?
--------------------------------------------------------------------------------------------------------
Suppose there is another doctor, C, who diagnoses 30% of all patients as positive.
C's diagnosis is independent of A's and B's.
2.4 Let X be the number of positive diagnoses a patient gets. Find the probability
mass function of X.

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman