In the problem of cancer (C) and tests (t1, t2), or any other example,
How can I calculate: $P(C^+|(t1^+ \text{ or } t2^+)$ I think this would be the same as finding: $$P(t1^+ \text{ or } t2^+|C^+) P(C^+)\over P(t1^+ \text{ or } t2^+).$$
But is $$P(t1^+ \text{ or } t2^+|C^+) = P(t1^+|C^+)+P(t2^+|C^+)-P(t1^+ \text{ and } t2^+|C^+)?$$
On the other side, is it true in other problems that $$P(t2^+|t1^+) ={ P(t1^+ \text{ and } t2^+)\over P(t1^+)}?$$
Thanks.