@ereliuer_eteer

Is Eve, when lying about what her name is, constrained to only be able to answer "I'm Ava"? Or is there a non-zero probability she'll give some name entirely different from "Ava" or "Eve" (which seems to be allowed)?

(it's clear that this makes a difference since if that latter probability is 1, e.g.., she *always* says "I'm Susan" when she's lying about her name, then "I'm Ana" + "yes" is both girls telling the truth with probability 1)

@ereliuer_eteer

Right, but we still need to know the probability that Eve will *say* she is Ava when she's lying. As things currently stand, all we have for the probabilities on Eve's possible responses to the first question are:

"I am Eve"
⟶ 0.25
(telling the truth)

"I am Ava"
⟶ 0.75x
(lying in one particular way)

"I am [neither Ava nor Eve]"
⟶ 0.75(1-x)
(lying some other way)

1/3

@ereliuer_eteer

The two possible scenerios that result in "I am Ava" + "yes", answers are that

(1) Ava is giving the first answer (0.5*0.75*0.25) and both are telling the truth,

(2) Eve is giving the first answer (0.5*0.75x*0.25) and both are lying

which makes the overall conditional probability (that they're both being truthful given that the answers are "I am Ava" and "yes") is 1/(1+x)

so we need to know what x is.

@ereliuer_eteer

seems to me that, for the problem to actually work (have a determinate answer), you want the first question to be, "Are you Ava?" rather than "What's your name?"

3/3