Given $P(C)$ and $P(A\mid C)$, what is $P(C\mid A)$? I am wondering if there's a way to find the solution if we know:
$P(C) = 0.01$
$P(A\mid C) = 0.7$
what is $P(C\mid A)$?
I think we need to know $P(A)$ to answer this question right? There is no other way around it?
Thank you!

Considering the given data, without knowing anything more, one may just write
$$
P_A(C)=\frac{P(A \cap C)}{P(A)}=\frac{P(A \cap C)}{P(C)}\cdot \frac{P(C)}{P(A)}=0.7\frac{0.01}{P(A)}=\color{red}{\frac{0.007}{P(A)}}.
$$
