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

Of the box you pulled the $100 or either box?

The box you already chose, you have a 50% chance.(you’ve already either selected box a or box b, a 1:2 choice)

If you can pick either box for second draw, you have a 66% chance of getting another $100 bill. (There are 3 bills remaining, $100, $100, and $1. You will get the $100 bill 2:3 times)

E: it’s an interesting problem because you have a statistically better chance to get another $100 if you have the option of switching boxes, even if you don’t utilize the option.

However it would always make sense to select the other box for your second draw, if possible.