What is harder to catch the faster you run?

Solve the puzzle by telling what does below picture means.

I have some blue and red sock in my drawer. I have a total of 4 socks. I pick 2 socks and the chance that I get a pair of red socks is 1/2.

What is the chance of picking a pair of blue socks?

Can you find out what is missing?

1 3 5
2 4 ?

Hint: It's not six. Think out of the box.

A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

I make two people out of one. What am I?

If you read clockwise, you can form a word by inserting three missing letters in the picture given below. Can you do it?

Solve the following series:
AZ, GT, MN, __, YB

John went to a parrot shop in Mexico, and the parrot owner told him that his parrot is so unique that he repeats everything he hears. John got excited and immediately bought the parrot. John went home and spoke many words, but the parrot does not repeat anything.
He went again to the parrot shop and complaint to the shopkeeper, but the shopkeeper never lied. Explain?

Can you write down eight eights so that they add up to one thousand?