## How to calculate combined probability of causally-linked events: joint probability?

Hello,

I'm a statistics novice trying to understand how to approach what I suspect is a fairly basic probability problem. I'd be very grateful for your patience and insight (and patience).

I'm trying to calculate the overall probability of two causally-linked events occurring. For example:*

What is the probability a member of the general population acquiring disease X and then dying from that disease?

I know the prevelance of disease X in the general population (1.2% of population acquire disease X), and I know the rate at which disease X causes death in the infected population (1.8% of infected persons die). *But I'm wanting to calculate is the overall probability of any given person in the general population acquiring the disease and then dying from it.

Am I correct in thinking that I'm just looking for the joint probability of disease plus death? *If so, is this how I'd solve it:

P(AB) = P(A | B) x P(B)
P(AB) = 0.018 x 0.012
P(AB) = 0.000216
P(AB) = 0.0216%

Am I on the right track? I feel like I'm not.*

I tried using Bayes' rule, but I gather is not relevant here because I'm not trying to modify confidence in a hypothesis in light of new evidence. Please correct me if I'm wrong in assuming this.

Note that I am*not*concerned with the accuracy of the diagnostic process. Most Bayesian examples I have encountered in my searching for solutions seem to focus on diagnostics.

Please forgive me if my questions are inane and basic. Like I said, I'm just starting out and am keen to learn more.

Thanks kindly for reading my query.

Jimi*