Puzzle #243: Five Nickels

You put five nickels in a bag. Four of them are ordinary nickels, but one is a fake with two tails sides. A random coin is drawn from the bag and placed on a table so only one side (which is randomly chosen) is showing. The coin shows tails. What is the probability that the coin drawn is not the fake?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 31, 2018 at noon Pacific Time. I will post the answer shortly after.