How does Murph know whether Dr. Brand is alive?

Question

In Interstellar the data transmission was only one way, that is, from The Earth to the spaceship, and not the other way, then how does Murph know that Dr. Brand is alive?

Answer 1

First of all, as explained in the answers to this related question, the data transmission isn't entirely one way. Remember, that they in fact got the signals from the first exploration missions (the 12 people visiting their respective planets 10 years ago) sent through the wormhole. For whatever reason those signals are rather simple, but they definitely got them, because they are the reason why they chose to visit those 3 planets only.

And given the fact, that due to the various time dilations at this point Amelia Brand had more or less just arrived at Edmunds' planet, she likely sent a new signal out from the planet. The humans at Cooper Station in turn received that signal, knowing that Amelia had arrived and the planet is Ok as a new home. The only problem that stands is how Amelia was able to send anything else than "rudimentary, simple binary 'pings' on an annual basis". But maybe she did really only get through that much and the humans on our side of the wormhole just assumed it was a sign that she was there.

An entirely different possibility (suggested by Hypnosifl in a comment to his related answer) is that they sent a probe through the wormhole to check for news and come right back (since the relay on the other end of the wormhole got and recorded every signal from the planets just fine). Afterall they were sitting in a space station near the wormhole and sending a probe through should be their smallest problem.