0
$\begingroup$

I have been practicing probabilities for quite some time now and i came across bayes' theorem. I've been sitting on this exercise for quite some time now and i am not completely sure if this is correct way to do it. i would love some more insight if the displayed solution is not correct

if a person is sick, the probability to diagnose the disease is 0.6. Probability for a healthy person to test positive for a disease is 0.02. Let's say 10% of population are sick people. What is the probability for a person to be healthy if he was diagnosed sick.

$P({\left(\text{positive}{\mid}\text{disease}\right)}) = 0.6$

$P(\text{no disease}) = 0.9$

$P(\text{disease}) = 0.1$

$P{\left(\text{positive}{\mid}\text{no disease}\right)} = 0.02$

${P}{\left(\text{no disease}{\mid}\text{positive}\right)}=\frac{{{P}{\left(\text{no disease}\right)}{P}{\left(\text{positive}{\mid}\text{no disease}\right)}}}{{{P}{\left(\text{no disease}\right)}{P}{\left(\text{positive}{\mid}\text{no disease}\right)}+{P}{\left(\text{disease}\right)}{P}{\left(\text{positive}{\mid}\text{disease}\right)}}}$

$\endgroup$
2
  • $\begingroup$ That will work when you substitute the numbers $\endgroup$
    – Henry
    Mar 23 '20 at 17:23
  • $\begingroup$ thanks for reconfirming $\endgroup$
    – woohoos
    Mar 23 '20 at 17:25
0
$\begingroup$

My standard method: Imagine a population of 10000 people. Since 10% of the population are sick, there are 1000 sick people, 9000 healthy people. 0.002(900)= 18 of the healthy people test positive and 0.60(1000)= 600 of the sick people test positive, a total of 618 people who test positive.

Of the 618 people who test positive, 18/618= 0.029, 2.9% are actually healthy.

$\endgroup$
3
  • $\begingroup$ that's what i tried, but wanted an example with bayes' theorem, before making any conclusions, will mark this as answered as the question is answered $\endgroup$
    – woohoos
    Mar 23 '20 at 17:37
  • $\begingroup$ I think there would be $180$ healthy people who test positive rather than $18$ $\endgroup$
    – Henry
    Mar 23 '20 at 18:01
  • $\begingroup$ Once again you are correct Henry, sadly I can't mark your comments as answers, thanks a lot for help $\endgroup$
    – woohoos
    Mar 24 '20 at 11:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.