♦️ ereliuer eteer ♦️Jan 6, 2023
Ava and Eve are identical twins, but Ava tells the truth with a probability of 0.75, and Eve tells the truth with a probability of 0.25 (independently of each other). Suppose, I meet them in the street and ask one of them: “Are you Ava or Eve?” and she responds “I'm Ava.” Then I ask the other girl: “Did she tell the truth?” and she responds “Yes.” What are the chances that both girls told the truth this time?
Show threadSibrosan

@ereliuer_eteer

0.5

If the first girl is Ava, they both must have told the truth; if she's Eva, they must have both lied.

And the probability of each option is the same, 0.75 * 0.25 = 0.25 * 0.75

Jan 7, 2023 at 11:57amWeb
Show threadMennoJan 7, 2023
@sibrosan @ereliuer_eteer
Ha! Your answer made me think it through. I think you're correct that it's 0.5. but it has nothing to do with their chance of telling the truth.
You started off right. The question is: what is the chance that both girls spoke the truth.
*If* the first girl is Ava, then they're both right. If the first girl is Eve, then she lied and it doesn't even matter what the 2nd girl said.
The chance of the first girl being Ava is 50/50.
Show threadSibrosanJan 7, 2023

"but it has nothing to do with their chance of telling the truth."

I think you're mistaken.
Suppose, as an extreme example, that the chance for Eve to speak the truth is 1, instead of 0.25.

In that case, given that both confirm the first girl is Ava, the chance of both telling the truth is 1, not 0.5.