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Simple coins (Posted on 2002-04-09) Difficulty: 2 of 5
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)

See The Solution Submitted by art    
Rating: 3.8750 (16 votes)

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re(3): Solution Using Real Prob/Stats | Comment 26 of 45 |
(In reply to re(2): Solution Using Real Prob/Stats by Eberhard)

HT and TH are "functionally equivalent" (as you put it) only if the function is "one coin is heads and one coin is tails".

If I flip two fair coins together a bunch of times, I will expect to get one of three outcomes:
(1) two heads, 1/4 of the time
(2) one head and one tail, 1/2 of the time, and
(3) two tails, 1/4 of the time

(I assume you agree with this so far.)
_______________________________

The problem states:
"at least one of the coins is showing up as 'tails'."

This rules out outcome (1).
Outcomes (2) and (3) are still possible.

The probability of those two outcomes have a 1/2 : 1/4 ratio, and the question asked what is the chance the outcome is (3).

(1/4) / [ (1/2) + (1/4) ] = (1/4) / (3/4) = 1/3
_______________________________

Please continue with your statistics class.
  Posted by SilverKnight on 2003-12-03 15:43:16

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