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