## ← 01-58 Cancer Test

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Showing Revision 2 created 04/13/2012 by Anna Chiara Bellini.

1. Let me ask you Bayes Rule in the context of a completely different example
2. to see if you understand how to apply Bayes Rule.
3. This time it's about cancer testing.
4. It is an example that is commonly studied in statistics classes.
5. Suppose there exists a certain type of cancer,
6. but the cancer is rare--only 1 in a 1000 people has the cancer--
7. where as 999 in 1000 people don't have it,
8. illustrated by the probability of cancer and the probability of not cancer.
9. Suppose we have a test, and the test can come out positive or negative.
10. The probability that the test triggers positive if you have cancer is 0.8,
11. and the probability that the test comes out positive given that I'm cancer free is only 0.1.
12. Clearly the test has a strong correlation to whether I have cancer.
13. Here's a really difficult question.
14. Can you compute for me the probability of cancer given that I just received a positive test.
15. Let me emphasize this is not an easy question, but you should be able,
16. based on what I've taught you, to calculate this result.
17. Think of the cancer/non cancer as the robot position
18. and think of the positive as whether the colored door observed is the correct one.