Friends here's an interesting problem :

A man possesses five coins, two of which are double-headed, one is double-tailed, and two are normal. He shuts his eyes, picks a coin at random, and tosses it. What is the probability that the lower face of the coin is a head ?

He opens his eyes and sees that the coin is showing heads; what is the probability that the lower face is a head ?

He shuts his eyes again, and tosses the coin again. What is the probability that the lower face is a head ?

He opens his eyes and sees that the coin is showing heads; what is the probability that the lower face is a head ?

He discards this coin, picks another at random, and tosses it. What is the probability that it shows

heads ?