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Old 10-06-2016, 11:41 AM
Ignotus Ignotus is offline
Join Date: Dec 2012
Posts: 978
Originally Posted by markn+ View Post
This problem is going to produce endless fruitless debate, because, like the boy-girl problem, the specified conditions are ambiguous. The details of the randomization procedure that produced the roll with at least one 6 have not been specified, so there are at least two possible answers, depending on how the roll was produced. I would plead with everyone who is about to reply here with the answer that seems "obvious" to them to read Wikipedia's article on the boy-girl problem first, to save a lot of pointless argumentation.

Here's one interpretation of the given problem:

"Two dice are rolled numerous times. In the cases where a six appears on at least one of the dice, the observer is told that one die is a six and asked the probability that the other is a six."
In this case, 25/36 of the rolls will not produce a six and are ignored. Of the remaining cases, 1 in 11 will have two sixes, so the answer is 1/11.

Here's another interpretation of the problem:
"Two dice are rolled once. It just so happens that at least one die shows a six. The observer is asked for the probability that the other is a six."

In this case the probability that the second die is a six is the same as the probability that any arbitrary thrown die is a six, 1/6.

Clearly different people in this thread are already interpreting the problem in different ways, and therefore producing different results.

Is the observer aware of us observing him? If so, does that knowledge somewhat skew his judgment?

Is my cat dead or alive?