Impossible exam question about conditional probability

[kristianlm]

Hi!

We are 3 students at RMIT who cannot understand how the following Artificial Intelligence exam-question can be solved:

There are 80% of meningitis patients who have the stiff-neck symptom. The probability of having meningitis for a person over the entire population is 0.02%.

a) What is the probability of a person being a meningitis patient if he/she suffers from stiff neck?

What we have so far is this:

P(S|M) = 0.8 P(not S | M) = 1 - 0.8 = 0.2
P(M) = 0.0002 P(not M) = 0.9998

a) is asking for P(M|S) -- right?

P(M|S) = (P(S|M)P(M)) / P(S)
P(S|M)P(M) are given and easy -- however, how can you find out P(S)?

P(S) = P(S | M)P(M) + P(S | not M)P(not M)

From what I can tell, it is impossible to find out P(S | not M) as this has not been given anywhere and cannot be derived from the already-given information. Or what are we missing out on?

We appreciate all help! Thanks!
Kristian LM

 

[pka]

There are 80% of meningitis patients who have the stiff-neck symptom. The probability of having meningitis for a person over the entire population is 0.02%.
a) What is the probability of a person being a meningitis patient if he/she suffers from stiff neck?
P(S|M) = 0.8 P(not S | M) = 1 - 0.8 = 0.2
P(M) = 0.0002 P(not M) = 0.9998

a) is asking for P(M|S) -- right?correct

It is impossible to find out P(S | not M) as this has not been given anywhere and cannot be derived from the already-given information.

You are correct about the lack of information.

 

[kristianlm]

Ok, that was what I was hoping ... thanks!

Kris