Suppose a card is drawn from a standard deck of 52 cards. Is it true that the events "get a heart" and "get a king" are dependent?
My professor told me it is true. I am not sure because $P(\text{get a heart}) = 13/52 = 1/4$ and $P(\text{get a king}) = 4/52$. Hence, $P(\text{Get a heart and get a king})= P(\text{get a heart})*P(\text{get a king}) = 1/4*4/52 = 1/52$. It is independent,right?
You're right. They're independent.
Another way to look at it: you have a $1/4$ chance of having a heart before or after knowing you got a a king. You also have the $1/13$ chance of having a king before and after you know you got a heart.
But as N.F Taussig mentioned, if you pull two cards, the events are dependent as no matter what card you get dealt first, it affects the chances of getting a specific second card.