FTM!! Just lost the rest of my plug

Hey just went the loo (tmi) sorry and when I wiped there was a big load of thick snot looking mucus, for the last few days I've been losing parts of my plug and I think the rest of it has just came out I'm 40weeks 2 days and got told last week I'm already 1cm an they could feel baby's head, I'm due to be induced tomorrow anyway but is there a chance labour could start on its own tonight?