There are 2 coins, one fair (heads/tails) and one unfair (head/head)
A person chooses randomly between the two coins, and throws it. the coin lands on head.
he throws the same coin again and it lands on head again.
he throws the same coin the third time and get tails
the question is what is the probability he chose the fair coin.
now, it sounds dumb as there is no tails to the unfair coin so the probability of him choosing the fair coin while twice landing it on head and third time is on tail is $1$
am I right? what is the math equation for this? I tried using bayes' law however I got confused with the 3 different throws.. Thanks!
The sample space of any outcome that results in tails for the unfair coin is 0, therefore it doesn't matter how many heads you toss in a row, if tails ever appears, then the probability that the coin you chose is the fair one is 1.0.