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?
You tossed two coins and chose to tell me that at least one was "tails". That's a different problem from "When two coins are tossed, what is the probability that they both show tails, given that at least one is showing tails?"
Consider four such situations, and they go exactly according to the probabilities involved:
On one occasion, you toss both heads, and report "at least one is a head."
On one occasion, you toss both tails, and report "at least one tail."
On two occasions, you toss one head and one tail. Now you have to choose which to report. Having no preference for one or the other, on one occasion you report "at least one tail" and on the other "at least one head".
In these four occasions, you twice reported "at least one tail." On one of those two occasions the other was heads; on the other it was tails.
Its 1/2 or 50%.
I, before your report, I had asked "is at least one a tail?" then when you reported in the affirmative, that would have indicated a 1/3 probability, because we would no longer be taking a random sampling.
Posted by Charlie
on 2003-02-21 08:40:30