Suppose that I have two coins in my pocket. One ordinary, fair coin and one coin which has heads on both sides. I pick a random coin out of my pocket, throw it, and it comes up heads.
- What is the probability that I have thrown the fair coin ?
- If I throw the same coin again, and heads comes up again, what is the probability that I have thrown the fair coin ?
- If instead of throwing the same coin again, I reach into my pocket and throw the second coin. If it comes up heads, what is the chance the first coin is the fair coin ?
[ Modified version of Meester, ex 1.7.35]
