Probability of $1 bill

Question

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)= $\frac{1}{3}$

Answer 1

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