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. (a) what is the probability that the lower face of the coin is a head? (b) he opens his eyes and sees that the coin is showing heads. what is the probability that the lower face of the coin is a head? (c) he shuts his eyes and tosses the same coin again. what is the probability that the lower face of the coin is a head? (d) opening his eyes, the man sees that the coin is showing heads. what is the probability that the lower face of the coin is a head?