We study mathematics because we cannot rely on our intuition!
Just try the question below and see what your intuition says.Then we solve them using mathematics!
Let’s say you have undergone a medical test.The test showed that you suffer from a rare disease that affects only 0.1% of the population. The doctor will tell you that the test is correct 99% of the time! do you really have the disease?
Since the test is 99% correct, most people would say that you have the disease, but the math says something else!
Let’s solve it!(Don’t worry, it’s really easy!)
We have received 2 information:
- the probability that you have the disease = P (D) = 0.1%
- probability that the test is correct = P (T) = 99%
Suppose there are 1000 people.
Since 0.1% of the population is affected by the disease and 0.1% out of 1000 people are 1, one of the above 1000 suffers from the disease.
(The red dot is who has the disease)
Now the probability that the test is correct is 99%.
which means that the test is incorrect in 1% of cases. 1% of the remaining 999 people are about 10 people. This means that 10 people (out of the remaining 999 people) are tested positive for the disease, even though they do not have the disease at all.
we need to find out what the probability of getting sick if the test is correct!
If you look closely at the image above, you will notice that you (the red dot) are 1 from a group of 11 points. In other words, the probability that you have the disease that the test results is 1/11. That’s about 9%.
I bet you never thought the chances were so slim!
Even more shocking is that if you repeat the test, the odds increase to 91%!
Do you see how bad our intuition is?and that’s why mathematics is important!
Thank you for reading!
P.S.If a doctor tells you that you have a rare disease, show him this calculation! He will start to question his entire medical career!
– (JK) Mr President, I would like to
This answer was inspired by a video on Youtube by Veritasium.The video is very interesting and very informative. Here is the link: