Probability summation help

#1
I have the following problem:

Two cups, A and B, each contain 1 ml of the same infectious serum. If there is a 30% probability that I will get the disease from drinking cup A and a 30% probability I will get the disease from drinking cup B, what is the probability of getting the disease if I drink both A and B?

I'm fairly certain I just add the probabilities. But I'm not sure because the cups contain the same thing. Thank you!
 

Dason

Ambassador to the humans
#2
Pretend for a second that instead of 30% the problem said 90%. Do you see an issue with your proposed approach?
 
#3
Yes, now I do see an issue with my approach. So does that mean it's a 30% probability no matter what because they are exclusive events?