Logic Riddles

Question: A woman is in the hospital for a routine procedure. The doctor leaves the room locking the door before he goes, the woman is alone. The doctor comes back to find the woman has died and there is another person is in the room. The door was still locked.
How is this possible?

Question: There are 11 bananas and you take 4, how many do you have?

Question: A rooster lays an egg at 6:00 AM. When does the farmer find it?

Question: John put a coin in a bottle and put a cork on the bottle and later managed to get the coin out without taking out the cork or breaking the bottle. How did he do it?

Question: There is a basket full of hats. 3 of them are white and 2 of them are black. There are 3 men Tom, Tim, and Jim. They each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim's hats, Tim can see Jim's hat, and Jim can't see anyone's hat.

Tom is asked what color his hat is and he says he doesn't know.
Tim is asked the same question, and he also doesn't know.
Finally, Jim is asked the question, and he does know.

What color is his hat?