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?


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?


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!