I toss two coins and look at the outcome. I then tell you that at least one of the coins is showing up as "tails". What is the chance that the other one is showing "tails" as well?

(from techInterview.org)

Well, this subject seems to have been covered multiple times in multiple ways- but the real answer and why are as follows: The first know that each toss is concidered a seperate event by probability (known as independence)- meaning that the probability of either coin showing a particular side is always one half 1/2. Second know that when trying to determine if both will be the same side the probabilities are multiplied, i.e. 1/4 (this can be thought of as an ordered sequence).

So-
Based on the information given in this question, the answer is 1/2 even though it seems like it should be 1/4. This is ONLY because we know that the one coin is tails, meaning that we must apply the principle of independece to determine the probability of the second be tails.

In order to simplify this- think of it this way-

I have two coins I filp them both and ask you to guess what they are-

1) I tell you one is tails and ask you to guess the other- where you clearly have a 1/2 chance of guessing correctly- this is the same as our problem

2) I tell you neither and ask you to guess both where your chances would be 1/2 * 1/2 = 1/4

Hope this clear up the confusion- I will post the more complicated math behind this if requested

Posted by Eberhard on 2003-11-26 12:50:30