Coin Head and Tail
I have two coins.
* One of the coins is a faulty coin having a tail on both sides of it.
* The other coin is a perfect coin (heads on side and tail on other).
I blindfold myself and pick a coin and put the coin on the table. The face of the coin towards the sky is the tail.
What is the probability that another side is also tail?
Among the four equally likely outcomes, three are favorable to “tails” and one of those three is favorable to “fair”. Hence Pr(fair∣tails)=1/3.
Since the up-facing side of the coin is Tail, the case that the other side also is tail is possible IF AND ONLY IF the selected coin is the faulty one. (Otherwise, the probability is 0, since the good coin can’t have both sides tails.)
Hence, the probability that this scenario happens is the same as the probability of picking the faulty coin between the faulty and good coins. Since there are only two coins in question, the probability of picking the faulty coin is 0.5.
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