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

Let’s stamp the bills.

The first box has one $100 bill and one $1 bill. Let’s put a red stamp on the back of the $100 bill and a black stamp on the $1 bill.

The second box has two $100 bills. Let’s put a green stamp on the back of one, and a blue stamp on the back of the other.

You pick a box at random, then draw a bill at random from the box.

What are the chances that the bill has a red stamp? 25%.

What are the chances that the bill has a black stamp? 25%.

What are the chances that the bill has a green stamp? 25%.

What are the chances that the bill has a blue stamp? 25%.

Oh wait, by the way, the bill doesn’t have a black stamp (it’s a $100 bill).

What are the chances that the bill has a red stamp? 33%.

What are the chances that the bill has a green stamp? 33%.

What are the chances that the bill has a blue stamp? 33%.

Note that you can only draw a second $100 bill from the box if the first $100 bill you drew had a green or blue stamp. So the chances of that are 66%.