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

Eli5 answer:

There are 3 $100 bills. You picked a bill randomly, meaning each bill had the same chance. But we know you didn’t pick the $1 bill. So, there’s a 1/3 chance you picked each one of the $100 bills.

There’s a 1/3 chance you picked the one in the box with the $1 bill.

The other box has two $100 bills, So there’s a 2/3 chance you picked one of those two.