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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?


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

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Solution re: Answer Comment 45 of 45 |
(In reply to Answer by Math Man)

I haven't looked at my Watch List in a while, and I'm back and the confusion on this puzzle seems to persist.

Let's assume the experimenter/interviewer conducts this test 8 times and the interviewer has no bias in favor of reporting heads or tails.

In those 8 trials, twice both coins will come up heads and the interviewer will have to say that at least one was heads.

In 4 of the 8 trials, one will come up heads and the other tails. Half the time (twice)  the experimenter will report at least one heads; the other half (again two of thet trials) at least one tails.

In 2 of the trials the experimenter will be forced to say at least one is a tails.

A total of four times, the experimenter said that at least one was a heads, and this is one of those occasions. On two of those occasions, it was because there were two heads. The probability is 1/2, assuming the experimenter has no bias in favor of reporting heads.

The puzzle does not state what the experimenter's overall strategy is or whether he/she has a bias--only that on this occasion he/she reported at least one heads. Certainly the experimenter can't truthfully say this all the time as sometimes both come out tails. One can only assume a random choice about which toss the experimenter reports.

  Posted by Charlie on 2014-07-06 10:46:13
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