Does anyone know where this hose goes to circled in red? I got a mini as a bday from girlfriend. I got it running but there is no hose on my carburetor where this hose is circled in red. Thank you all in advance!

Well I guess it’s not going to let me upload a photo but the hose in question is the one that attaches to the top of the carb next to the fuel line. Mine is missing 

Welcome from NZ. Posting pics is a problem i believe until youve had multiple post. Strange i know, but we live with it & must post via an external provider. i just put a link to my google photos but most use "imgur" . Anyhoo--i had 3 or 4 JT's over the years & with those fully enclosed carbs there will be a breather from the bottom of the bowl that has the vent to the outside via a small hose directly below the bowl & out through a small hole it the case--straight down Maybe another side vent high up cant remember now but thats ok left within the cavity. #33 is probably it in the link. Doesn't need to protrude far out side the case. www.partzilla.com/catalog/yamaha/motorcycle/1971/jt1/carburetor

10-4, thank you. That was another question I had. The hose I am referring to would go on the barb adjacent to the fuel line. So directly next to #13

files.semestergas.se/Yamaha_Mini_Enduro/...82nd_ed._1976%29.pdf
Must just be a breather into the bowl. Can't think what else it could be
Couple of images here of the internet.
photos.app.goo.gl/MTsfnjdWYZ71bmx5A

Here's a snapshot out of someones video. He calls it a bowl vent so it'll just go up the airboot a reasonable distance. I'll link his video. I'm outa here now for a bit.
photos.app.goo.gl/NLM6zqEgzdE7jDDM7
Here's the video, not sure it'll help but!!

Here is a photo I had on my phone showing the hose you mention. I also believe it is a vent and I believe the open end is tucked into the base of the air cleaner housing. I’m out of town so I can’t take any additional photos right now.

imgur.com/a/oISrmrM

EDIT
Sorry Morley. I didn’t notice that you linked an almost identical photo…..

All good Schu. Love JT1's. I shortened up the suspension front & rear on one of mine 50 years ago so one of my kids could reach the ground. Eldest son--now 56 was riding his at 4 year old. 

I seen on that too on the 1972 model that the hose goes to the air cleaner housing. I can’t see where in the housing it would go on the 71 since it’s a different housing. 

Pretty sure the float bowl vent hose doesn't really "go anywhere", as was already said it just tucks up into the air filter a bit.  They did that to get the venting point away from the "intake pulsing" in that little chamber which could mess with carburetion.