Probability of $1 bill Suppose you have a wallet that contains either a 1 bill or a 10 bill (with equal probability). You add a 1 bill. Later you reach into your wallet and randomly remove a bill. It's a 1 bill. What's the probability that the bill remaining in the wallet is a 1 bill? This is all I have so far: A= event that $1 bill is chosen B= event that $10 bill is chosen P(A) = $\frac{2}{3}$ P(B)= $\frac{1}{3}$

Well, you have two possible configurations before the draw. Enumerate those possibilities with the possible draws from each:

* 1 & 1
* draw first 1
* draw second 1
* 1 & 10
* draw 1
* draw 10



Consider the draws here where you took out a 1... you can count how many second draws will result in a 1 versus a 10.

Related: check out the famous Monty Hall problem