99 percent accurate. Really!

Today I threw an interesting challenge to the students to sensitize them on misleading nature of accuracies reported in some medical literature.

Question: A type of cancer can be contracted by 1 in 10000 people. A patient was tested positive for it by a test which gives 99% accurate results. What is the probability that the patient actually has the cancer?

Answer:

As you can see the probability of having the cancer turns out to be less than 1% even with a 99% accurate test.

But it doesn’t mean that the test is useless. Let’s see what happens when we repeat the test just one more time.

Question: After testing positive for cancer if the patient repeats the tests and is found to be positive for cancer again. Now what would be the probability?

Answer:

We can see that just by having one iteration of the test we can take the confidence to 50%. So sometimes a second opinion is necessary!

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