Probability of C after event A and B have occured **Event A:** Cardiac arrest **Event B:** Death of cardiac arrest Assuming $1$ in $1000$ heat-strokes lead to a cardiac arrest ( **A** ) $1$ in $100$ cardiac arrests lead to death ( **B** ) What is the probability of cardiac arrest leading to death due to a heat stroke ( **C** ) ? I was thinking this formula applies: I calculated $0.01$ ($A$ and $B$) / $0.001$ ( **A** ). The result is $10$ which cannot be correct. Where lies my mistake / thinking error ?

It's much more intuitive than that. If $1$ in $1000$ heat strokes lead to a cardiac arrest, the probability of cardiac arrest due to a heat stroke is $0.001$. Similarly, the probability of death after a cardiac arrest is $0.01$. Since **A** and **B** are independent events, the probabilities multiply. So the probability of the event " _cardiac arrest leading to death due to a heat stroke_ " is

$$ 0.001\times0.01 = 0.00001. $$