A probability problem was posed to me, and I am terrible at probability. It was first posed to me like this:
I have 5 coins. One of them is a two-headed coin, and the others are normal coins. I pick a coin, and then I flip that coin three times; each time is heads. What is the probability that the coin is two-headed?
My answer was, naturally, 1/5. I am still of the opinion that it's the correct answer to that particular phrasing (do you agree?). But of course I was told this is a wrong answer. After some thought, I came up with the following phrasing which is what was really meant:
You are given a coin and told that it has a 1/5 chance that it is double-headed, otherwise it is a normal coin. You are allowed three flips of the coin. Upon doing these, you receive three heads. What is the probability that your coin is double-headed?
Now I have two questions, first of all does that seem like a proper rewording to you? And secondly... What is the answer and the reasoning to reach that answer? I am terrible at probability, and while I can clearly see the problem and maybe spell out the first step or two, I am at a total loss as to how to arrive at an answer.
Edit: one more question, actually: is this an instance of the Monty Hall problem? I obviously see that it is very different, yet it feels somehow similar...