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

Are you always picking the second bill from the same box as you pulled out the initial $100, or shuffling them up and picking at random again? The math is very different in either case.

When talking probabilities the exact wording of the question matters as well.

“What are the chances I pick $100 from a random box then $100 again in the next pick”

vs

“If I pick $100 from a random box, what are the chances I get $100 again in the next pick”

Have very different meanings.