Captain reported the First Officer read an old page from their QRH which resulted in incorrect landing data for the aircraft.

Narrative

We were on final for Runway XXR at ZZZ. I called for AUX HYD ON; gear down per our checklist. The First Officer (FO) complied; and we got on amber R INBD BRK FAIL CAS. I told the FO to ask for delay vectors; then asked her to run the checklist in the QRH while I took the radios. I also put the autopilot on and continued to comply with ATC instructions while monitoring her as she ran the checklist. Basically it had us put the gear up; pull and reset a CB; then put the gear back down to see if the CAS message went away. We did this; and the amber message went away and was replaced with a white BRAKE FAULT CAS. She asked if she should run that checklist; and I told her to finish the one that we were on first. The next step on our amber checklist was that if the message extinguishes; the checklist is complete. She read this out loud; and I told her to go ahead and run the checklist for the white CAS. She did; and it basically said that there was a minor degradation in the system and to add 500 ft to the landing distance. We did this; and still had plenty of runway to continue to ZZZ. We asked for vectors back to the approach; and landed without further incident. After we landed; I asked her to run back through the checklist with me so that I could explain to maintenance the steps that we had taken. When I opened the QRH; there was a yellow updated sheet for the amber message on the left as well as the old white one right. I started reading off of the new yellow sheet; and she stopped me and told me that she had actually done the outdated white page. We looked at the differences between the two; and the updated sheet is similar; but it adds that 1) no action is required for the white BRAKE FAULT CAS; and 2) that even if the amber CAS goes away; normal brakes might not be operational and that we should refer to amber tab 42 for the emergency brake landing checklist (which we had not done since it wasn't referenced on the page that she had been looking at). Looking amber tab 42; there were 3 things that we hadn't done as part of our normal SOP's. These were to recalculate the landing numbers with anti-skid off; L&R IGN on; and to brake with the emergency parking brake instead of normal brakes. I ran the landing numbers with the anti-skid off later that night; and with 60% numbers we really needed an 8;700-9;000 foot runway (the LDA for XXR at ZZZ is 5;XXX ft). The FO immediately understood the mistake and the potential consequences; and she felt really badly about it. Obviously no one was hurt in this instance; but if the brakes had really failed it's very likely that we would have run off the end of the runway. As the Captain; it is my responsibility to ensure that the correct checklists are being run. We do kind of cover this in the sim at recurrent training; but you usually know if the Pilot Monitoring (PM) is running the wrong checklist because we've just done the same one 12 times in the last 2 days. As far as I am aware; we don't have a procedure for verifying that the PM is doing the correct checklist. I'm not sure if there is an ideal way to do this in every situation; especially if the Pilot Flying (PF) has their hands full. In the future; I will make sure that I physically look at the checklist that they are doing (or that they look at the checklist that I am doing) if the situation permits. I do think that to some extent you do have to just trust that the other person knows what they are doing and that they are following their training. I do also think that it would be beneficial to maybe pull a QRH out of a plane during our company indoc/recurrent and run through a couple of scenarios. Or; to add a random emergency that requires a checklist procedure to our sim training so that we get experience with checklists that are outside the norm for us. Also; I'm not sure if the outdated white page should have been removed from the QRH when the yellow update was added?