quizexe1 - Now suppose that your test comes back positive....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT 427 Quiz/Class Exercise 1: With Solution A Cancer Screening Test : Suppose a screening test for a particular type of cancer is about to be given to a homogeneous group of persons, including you, who exhibit no symptoms of the disease. It is known that the chances that you, as a randomly selected member of this group, have this type of cancer are Fve in 1 , 000. Suppose the conditional probability that the test will give a positive result (indicating the presence of cancer) given that you have cancer is . 95, and the conditional probability that the test correctly indicates no cancer given that you are free of the disease is also . 95. Thus, the test is about 95% accurate both for persons with and without the disease.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Now suppose that your test comes back positive. What you want to know is, what are the chances that you have this type of cancer? A common wrong answer – that the chance is about . 95 – is very much wrong! Solution: Let A 1 = Has Cancer A 2 = Does not have cancer Clearly, P ( A 1 ) = 5 1 , 000 , P ( A 2 ) = 995 1 , 000 and B = Tested Positive With P ( B | A 1 ) = . 95 , P ( B | A 2 ) = . 05 By Baye’s Rule P ( A 1 | B ) = P ( B | A 1 ) P ( A 1 ) P ( B | A 1 ) P ( A 1 ) + P ( B | A 2 ) P ( A 2 ) = . 95 × 5 1 , 000 . 95 × 5 1 , 000 + . 05 × 995 1 , 000 = . 087 That is, even your test comes back positive, the chances you have this type of cancer is just 8.7%. 1...
View Full Document

This note was uploaded on 04/16/2010 for the course STAT 427 taught by Professor Staff during the Spring '08 term at Ohio State.

Ask a homework question - tutors are online