it depends on how many coins are in the hat. if there's 2 coins in a hat then the probability of picking either of them at random is 50% regardless of if they are fair or bias.
P(f) = f/n
P(b) = b/n
A hat contains n=f+b coins, f of which are fair, and b of which are biased to land heads with probability 2/3. A coin is drawn from the hat and tossed twice. The first time it lands heads and the second time it lands tails. What is the probability that it is a fair coin ?
I am not really sure where to start..
The probability of choosing a biased coin and obtaining HT from 2 throws is
the probability the coin was fair is the fair coins probability divided by
the total probability for this scenario.
Therefore the probability the coin was fair is