Does mutual exclusivity mean dependence? I have read on several posts including here that mutual exclusivity of two events mean that they cannot be independent. However, does that mean that they are dependent? I'm not sure if I'm understanding this correctly.
I have a problem where there is a deck of 10 cards, and two of them are marked with a symbol. I am drawing two cards consecutively without putting them back in the deck. I am asked to calculate the probability of A (the event that the first card is marked), the probability of B (the event that the second card is marked), and the probability of (A intersect B).
I am thinking that events A and B are dependent because if A does happen, the number of marked cards remaining changes, changing the probability of B. Also, I think that they are not mutually exclusive because A and B both can happen. What am I missing here? How am I supposed to calculate P(B) if I am not given the information about the first draw?
 A: 
I have read on several posts including here that mutual exclusivity of two events mean that they cannot be independent. However, does that mean that they are dependent? I'm not sure if I'm understanding this correctly.

Correct, mutual exclusion infers dependence except in the cases of null events.   Because mutual exclusion means $\mathsf P(X\cap Y)=0$ and unless either one of those events has zero probability measure, then $\mathsf P(X\cap Y)\neq \mathsf P(X)\mathsf P(Y)$ which means they are not-independent.

I have a problem where there is a deck of 10 cards, and two of them are marked with a symbol. I am drawing two cards consecutively without putting them back in the deck. I am asked to calculate the probability of A (the event that the first card is marked), the probability of B (the event that the second card is marked), and the probability of (A intersect B).
I am thinking that events A and B are dependent because if A does happen, the number of marked cards remaining changes, changing the probability of B. Also, I think that they are not mutually exclusive because A and B both can happen. What am I missing here? How am I supposed to calculate P(B) if I am not given the information about the first draw?

You are missing nothing.   The events are indeed dependent but not mutually exclusive.   That is okay.
To find $\mathsf P(B)$ think of it this way:  I take the ten cards and draw two in turn, placing them face down on the desk, then I point at the second card and ask: "What is the probability that this is one of the two marked cards?"

 $\mathsf P(B)=2/10$

The probability of $A$ is found similarly.   However, the probability of the intersection, $A\cap B$ is not the product of the two (as they are dependent).   It is the comparison of the count of ways to select the two marked cards versus that of the ways to select any two cards.

 $\mathsf P(B)=\binom 2 2/\binom {10}2$

