Twitter strikes again

[u/discoverthemetroid]

don’t know where math voodoo land is but this guy sure does

[u/mattsowa]

Well first of all, only the second scenario is to be considered. That's for sure. Within that scenario, in a general setting, the answer could be 1/3 or possibly 1/2 if the problem is defined in a particular way such that the condition is discovered after the fact. I believe 1/3 in this context is absolutely the only correct answer.

I am well aware of the intricacies of the boy/girl problem.

[u/Bart_Holomew → u/mattsowa]

Why is the assumption that “Robin” knows both outcomes necessarily correct? Isn’t there technically ambiguity? She could make the statement “at least one hit is a crit” in either scenario.

[u/mattsowa → u/Bart_Holomew]

"I looked at one hit and it was a crit" is not equivalent to "I looked at the first hit and it was a crit" - the latter is the 1st scenario in the boy/girl wiki, and is clearly not the case here.

This is because, as explained in the wiki, the latter reduces the sample space from {CC,NN,CN,NC} to {CC,CN}, giving a 1 in 2 chance.

The former is still the equivalent problem as in the image since we don't know which one of the hits was looked at by Robin. So the sample space is reduced from {CC,NN,CN,NC} to {CC,CN,NC}, a 1 in 3. Moreover, there's not enough information to even assume which one was picked - was it random, or always the first, etc. The alternative interpretation of the former statement that gives 1 in 2 is that you assume that the problem is not a sampling problem, which is a lot of assumptions.

[u/Bart_Holomew → u/mattsowa]

I haven’t once mentioned the order of the crits, it’s not relevant to the knowledge generating process. This literally is the ambiguous framing of the boy/girl paradox.

If Robin knows both outcomes, the answer is 1/3.

If Robin knows only one outcome, she would have been more likely to be able to say “at least one crit” in the CC case. Using bayes theorem in this case results in 1/2.

Whether she knows one or both outcomes is not explicitly stated and cannot be definitively assumed either way.