Flipping either a biased or unbiased coin Here's a question I was faced with recently: > I have an unbiased coin with one head side and one tail side, and a biased coin with two tail sides. I choose an coin whilst blindfolded, and flip the coin. The result is a tail. What is the chance that the coin is biased? What is obvious is that I have a 50% chance of picking the biased coin to begin with, but what I am not sure about is whether or not the result of the flip affects the chance that I picked the biased coin. Any help?

This is easier to see if you extend the experiment and pick a coin and flip it say $100$ times. You would expect output like:

$$HT_uTTTT_uHTT_uHT\dots THHT$$

with a probability table:

$$ \begin{array} {c|c} H&0.25\\\ T_u&0.25\\\ T&0.5 \end{array} $$

If you throw a tails, $2/3$ times it will come from the biased coin, so if you say 'biased' every time tails appear, you will be right $2/3$ times.