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)

(In reply to re(3): Solution Using Real Prob/Stats by SilverKnight)

SK, I don't know if you've had a chance to look over the full set of comments on this, but this problem is a particular bugaboo of mine. The salient point is the full quote from the problem--not "at least one of the coins is showing up as 'tails'." but "I [the narrator, who has just tossed the coins] then tell you that at least one of the coins is showing up as 'tails'."

Suppose the narrator has done this 4 times--no, make that 8 times-- and it has come out, strangely enough, exactly the number predicted theoretically:

HH and the narrator reports at least one head.
HH and the narrator reports at least one head.
HT and the narrator reports at least one head.
TH and the narrator reports at least one head.
HT and the narrator reports at least one tail.
TH and the narrator reports at least one tail.
TT and the narrator reports at least one tail.
TT and the narrator reports at least one tail.

Out of the 4 times that the narrator chose to say at least one is a tail, in 2 cases (or half the time) both are tails.

While the narrator is not saying a particular coin in the sense of "the first one" or "the one that's a nickel", etc., he is in effect saying, "the one about which I choose to report." By putting in the form of a narrative story, rather than a puzzle statement, the dynamics change to what I have mentioned here.

Posted by Charlie on 2003-12-03 22:00:28