Question

Say I have a wallet that contains either a $5 bill or a $20 bill (with...

Say I have a wallet that contains either a $5 bill or a $20 bill (with equal likelihood), but I don’t know which one. I add a $5 bill. Later, I reach into my wallet (without looking) and remove a bill. It is a $5 bill. There is one bill remaining in the wallet. What are the chances that it is a $5 bill?

Math   Statistics-And-Probability   
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Answer #1

Assuming $5 bill or a $20 bill with equal likelihood initially

We use Bayes Law

P ( initial bill in the wallet was $5 | the first bill drawn was $5 ) =

[P ([first bill drawn was $5 |initiall bill in wallet was $5 ) * P (initial bill in wallet was $5 ) ] / [P ( first bill drawn was $5 | initial bill in wallet was $5)*P ( initial bill in wallet was $5 ) + P ( first bill drawn was $5 | initial bill in wallet was $20) * P ( initial bill in wallet was $20 ) ]

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