Did Hope know her blood would heal Jossie Saltzman?

In Legacies S01E16 "There's Always a Loophole," Hope went to the Triad Organisation's place (in GA) to save Landon. After she reached there, Landon told her about Malivore and its/his history, might have mentioned in his story how Malivore was formed/created with Wolf-Vamp-Witch blood.

I suppose after knowing this (the Wolf-Vamp-Witch blood thing), she figured out that she is the key for Malivore's end.

But my question is, how did she know (not guess) that her blood would heal Jossie's wound? It was not her guess for sure because she said to Alaric, "I'll explain it later". There was no way she could have known that Malivore was a creation of tri-breed type blood.

Also, if she knew already, why didn't she give her blood to Jossie herself when they were in the cell, captured by Triad people at school?

Because you are missing the major point. Hope was also shot with the Malivore mud bullet, as she had the mark on her cloth but she was not affected by it and she noticed it while stopping blood fountain while next to Alaric. And she was not affected by the Malivore memory wipe after Landon's mother jump.

So she figures out that it do not affected her, so she suggested her blood for a cure.