If there are two boxes. The first has a 100$ bill and a 1$ bill, and the second has two 100$ bills. If I puck a random box and take out a 100$ bill, whaat is the chance of me taking out another 100$ bill?

Question

I’m honestly stuck. I’ve seen people say 1/2, others 2/3. Something Monty Hall Problem, Bayes Theorem but I’m still confused so here I am.

Edit: I believe you are not allowed to change your box choice on the 2nd “turn” as that would make having two boxes pointless, wouldn’t it?

In: 10

Answer 1

It would really help if the question was specified precisely. It’s highly ambiguous at the moment. This is how I interpret the question.

You pick one box at random. You take one note from that box at random. What is the probability that the other note in that same box is a $100 bill?

Another comment spells out the possibilities nicely:

>1:You pick the box with a $1 and $100 bill and draw a $1 bill

2:You pick the box with a $1 and $100 bill and draw a $100 bill

3:You pick the box with two $100 bills and draw the first $100 bill

4:You pick the box with two $100 bills and draw the second $100 bill

We know that 1. is not possible since you picked a £100 bill, so there are only 3 paths you could be on. In one of them (2), the other bill will be £1. In two of them (3 and 4) the second bill will be £100. Therefore the probability is 2/3.

This is an example of conditional probability using Bayes’ theorem, but in this case it’s simple enough to explain without the formula.