I am getting confused with these probability questions, could you help explain the following:

A bag contains 4 coins. You are told that one of them is a normal coin; however, 1 coins aredouble-headed (i.e., both sides are heads), and 2 is double-tailed.The coins cannot be distinguished unless you check both sides of a coin.

For each of the following question, you pick out a coin C from the bag uniformly at random.

(1) You toss C for 1 time.What is the probability that the lower face of the coin is heads?

(2) You check and see that the upper face of the coin C is a head. What is the (conditional) probability that the lower face is head?

(3) You toss C for 1 time and the lower face is head. So You toss the coin C again. What is the (conditional) probability that the lower face is still head?

(4) If for the 2tosses of C, you seeone head and one tail for the upper face. Which coin would you guess (normal, double-headed, or double-tailed)? What is the probability that you are wrong?