Computability of a probability theory problem [closed]

Question

This is a problem I solved for a course and I was wondering if my solution is correct. I wouldn't normally post a pure mathematics problem, except that I believe that is is incomputable, and hence a computer science problem.

You are given:

P(S) = 10%

P(Theta1 | S) = P(Theta2 | S) = 96%

P(not Theta1 | not S) = P(not Theta2 | not S) = 98%

and no other information besides the usual axioms and definitions of probability theory.

In particular you are given no information about the independence of events.

You are asked to compute P(S | Theta1 and Theta2).

Is this solvable? If not, provide an incomputability proof.

Interesting, hey?

Answer 1

No, it's not solvable without an assumption, such as Theta1 and Theta2 being independent.

However, that's not what computability means.

The problem is that you need a term of the form P(Theta1 and Theta2), but there's no way to get that without knowing how correlated they are.