Estate said:
I find it hard to put an exact number on it.
I say 50/50 because it's a sort of all or nothing... She will either be left impressed and intrigued as to who you are and want to know more... or she'll just think you were some randomer and not really be too bothered to follow up unless your followup is impressive.
Are you just asking though because it happens you sometimes or is this the game you follow?
Personally I DO like the approach of just going in, quickly talking to her and getting the number if it's not a situation where like in a bar where I can hang around and escalate... but 1 minute is very quick... even 5 minutes would increase your chances much more. At least in a few minutes you can impress her with some fun banter or talk she might remember you.
The key to a quick number is just to be memorable. Guys have different styles as to how to be memorable so I won't go into that now.
But I walk through the city on any given day... I am approached by 10 people looking for money or a cigarette just on my way to work. Probably 5 more looking to sign me up for some charity or something... but occasionally one of them or some street performer comes right up and says something funny or is very animated or stands out somehow... maybe I'll smile and walk on but I'll remember that funny guy later in the day but none of the others.
I'm asking because that's what I like doing, yes.
I like walking around minding my business, even walking with the same person for a long way, unless she's really interesting -and in that case it would be a great pleasure but that's rare!-, I'd feel like I'm tying myself down too much

.
I said one minute just to convey the message of "quickness", can even be 2 of course, and even 5

, but the kind of person I am, most of the times I'd rather not spend a whole afternoon with an unknown person

.