# How can I compute the probability of this?

I have a question about something that is asked. I've read to make a table of this by using a very large number (like 100.000), but I actually don't know where to start.

Suppose that there was a cancer diagnostic test that was 95% accurate both on those that do and those that do not have the disease. If 0.4% of the population has cancer, compute the probability that a tested person has cancer, given that his or her test result indicates so

Can someone please give me some directions? I want to understand what they mean...

What I had was that 400 people have a disease, given the fact that a test would be 100% accurate. Because it is 95%, I have "people with a disease" is 280... I mean, am I going the right direction with this?

If someone can show me how to calculate and put it in a table, I would be grateful.

The epidemiology says, 0.4% have cancer, that is in a table:

                test says
yes       no      sum
true    yes                       0.4 %
cancer  no                       99.6 %

sum                      100 %


The test is right in 0.95 of the cases and wrong in 0.05, thus

                      test says
yes          no         sum
cancer  yes     .95*.4%      0.05*0.4%    0.4 %
no      0.05*99.6%   .95*99.6%   99.6 %

sum                               100 %


This is enough to answer the question, but you will probably need to fill the rest of the table for the questions still to come.

• Thanks! I'd preferred doing it with absolute values instead of percentages, but thanks. I'll sort it out. – Siyah Nov 21 '16 at 15:28

You shouuld also take into account the Bayes' Theorem to justify your answer.

https://betterexplained.com/articles/an-intuitive-and-short-explanation-of-bayes-theorem/

Try to understand it and consider the events:

A) Have the dissease

B) Have a positive diagnostic