You are a member of a data science team of a major cancer specializing hos- pital. To plan resources (beds, personnel etc.) one of the metrics you are asked to estimate is the probability of a patient having cancer given a positive cancer screenings test result. Your manager told you to call this probability p(cancers+) has given you the data you need: 1. 1% of women have breast cancer (and therefore 99% do not). 2. 80% of mammograms detect breast cancer when it is there (and therefore 20% miss it). 3. 9.6% of mammograms detect breast cancer when it's not there (and there- fore 90.4% correctly return a negative result). While asking around for anyone that has done this before, a colleague of yours is giving you several hints: "Luckily, your manager gave you the prior probability p(cancer)" • "Just use the Bayes rule p(ab) = p(ba)p(a)/p(b) and you will be OK".

You are a member of a data science team of a major cancer specializing hos- pital. To plan resources (beds, personnel etc.) one of the metrics you are asked to estimate is the probability of a patient having cancer given a positive cancer screenings test result. Your manager told you to call this probability p(cancers+) has given you the data you need: 1. 1% of women have breast cancer (and therefore 99% do not). 2. 80% of mammograms detect breast cancer when it is there (and therefore 20% miss it). 3. 9.6% of mammograms detect breast cancer when it's not there (and there- fore 90.4% correctly return a negative result). While asking around for anyone that has done this before, a colleague of yours is giving you several hints: "Luckily, your manager gave you the prior probability p(cancer)" • "Just use the Bayes rule p(ab) = p(ba)p(a)/p(b) and you will be OK".

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section: Chapter Questions

Problem 14T: An unbalanced coin is weighted so that the probability of heads is 0.55. The coin is tossed ten...

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