(a)A gambler has a fair coin and a two-headed coin in his pocket. He selects one of the coins at random; when he flips it, it shows heads. What is the probability that it is the fair coin? (b) Suppose that he flips the same coin a second time and, again, it shows heads. Now what is the probability that it is the fair coin?
answer to (a) is 1/3 which you need for (b), the answer to (b) is
I learned the basics of Bayes, but I don't understand what it means to have $O_1$ and $O_2$
Problem (c)) Suppose that he fluids the same coin a third time and it shows tails. What's the probability that it is the fair coin? How do we solve this?