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posted by  mandingo on 10/5/2008 12:08:35 PM  |  status: Live  

Conditional probability. I always rate lifesaver!

Course Textbook Chapter Problem
Statistics and Probability N/A N/A N/A
Question Details:
Say I have a wallet that contains either a $2 bill or a $20 bill (with equal likelihood), but I don't know which one.  I add a $2 bill. Later, I reach into my wallet (without looking) and remove a bill.  It's a $2 bill. There's one bill remaining in the wallet. What are the chances that its a $2 bill?
 
 
I got 2/3 but I am not confident with that answer.
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Sage
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posted by James Kissinger on 10/5/2008 12:43:10 PM  |  status: Live
Asker's Rating: Lifesaver   
mandingo's comment:
"but there are 3 possible $2 removals and 2 where a $2 remains, isn't that 2/3?"
Response Details:
Consider the 2 possible situations. If the bill was $2, then after you put in $2 and take out a $2, it's going to be $2 in there.
If the bill was $20, then after you put in $2, and take out a $2, then it's going to be the 20 in there.

Since the two have equal likelihood, the answer is 1/2.

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