What is the probability that other coin shows tails?
In a class on probability a statistics professor flips two balanced coins. Both fall on the floor and roll under his desk. A student in the first row informs the professor that he can see both the coins. He reports that at least one of them shows tails.
The statistics professor flips two balanced coins, each of which has an equal probability of showing heads or tails. The coins fall on the floor and roll under the desk where they are visible to a student who reports that at least one of them shows tails. The probability that the other is also tails has to be determined.
According to the student at least one of the coins shows tails. This is possible in 3 different ways, TT, TH and HT. The student may be referring to either the coin that shows heads or the coin that shows tails.
If the coins land to show TT, which has a probability of (1/3), the probability that the other is also tails is also (1/3). If the coins land to show TH, of which the possibility is (1/3) and the student is referring to the coin that shows head, which has a probability (1/2), the probability that the other is tail is (1/2)(1/3) = 1/6. This applies to HT also.
This gives the probability that the other coin shows tails as (1/3) + 2*(1/6) = (1/3) + (1/3) = 2/3
The required probability is 2/3.