Saturday, April 28, 2012

On Mathematics...

A recent post by that somewhat superficial appellation of a “Facebook Friend” presented the following problem:

“There are 2 Identical Hotels (“A” and “B”) next to each other.  Both of the buildings contain 100 rooms numbered 1-100.  110 guests are blindfolded and randomly put into rooms 1-10 of building A, and rooms 1-100 of building B.  You are one of those people, and you are told that your room number is 9.  What is the probability that you are in building A?”

My response:  “I am blindfolded and “someone” tells me I am in room 9?  The answer is 50/50, because I don’t believe what I am told given that I am blindfolded and it is unclear from the problem exactly what type of situation I am in”.

Yes, readers, I am aware that this can be solved with some Bayesian calisthenics (what is the probability of being in hotel A if someone says you are in room 13?...0%, etc.)  But context is everything and it’s that most luxuriant tapestry that provides the fabric for real answers to every meaningful question.

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