What is both possible and impossible at the same time?

There was a blind man. He had four socks in his drawer either black or white. He opened it and took out two socks. Now the probability that it was a pair of white socks is 1/2.

Can you find out the probability that he had taken out a pair of black socks ?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

You have two rectangular wires.

Both of them have property that when you light the fire from one end , it will take 60 minutes to get completely burn.

However, they do not burn at consistent speed (i.e it might be possible 1st 20% burn in 50 minutes and 80% can burn in 10 minutes).

So how could you measure 45 minutes ?

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

A man embarked on a questionnaire game. He kept asking the same question to whomever he found. The answer each time was different.

Can you guess what the question was?

In which direction should the missing arrow point?

He digs out tiny caves and stores gold and silver in them. He also built bridges of silver and made crowns of gold. They are the smallest you could imagine. Sooner or later everybody needs his help, yet many people are afraid to let him help them. Who is he?

The below mentioned letters have been placed in a order using a logic.

DEAD, BALL, FEAR, SHOP

Can you find the logic?

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?