[maytc]

Never liked the way these problems are worded.

`You take a random ball out of the urn—it’s red—and discard it.`

How normal people read it: Given this specific instance where you just discarded a red ball from this urn, what's the probability of the next ball?

How it expects you to read it: Given infinitely many random samples from the urn. For cases where you get red, remove it, then take a second sample. What's the probability of the next ball, given all the samplings?

[feoren]

Both of those have the same answer. Why would they not?

[zarzavat]

I would go further and say that the second reading is in fact incorrect interpretation of the problem in the English language. Being a mathematician doesn’t give some special right to gaslight people on their knowledge of English.

This problem is in a similar category as badly explained monty hall problems where the statement of the problem is so bad that it ends up changing the answer.

For example I have seen the Monty hall problem stated in popular media like this:

“There are three doors, behind two are goats and one is a car. You choose a door at random and there’s a goat behind it. You choose another door, but before opening it the host asks if you want to switch your choice. Is it more profitable to switch or to stick or does it have the same chance?”

Of course it doesn’t matter. This is actually a good way to trick inattentive mathematicians who pattern match on the problem but don’t actually read it.

[lencastre]

Love this, can we mangle the problem some more? Like, you open one door and it’s a goat, the host then says he will open another door containing the trip to Bali. Do you want to open the other door or stay with the goat you already have?

[bobbylarrybobby]

But those two readings have the same answer?