The whole bar is every ball in the bag — the event slice plus the "not event" slice always fills it.
Chase:
P(red)
3/8
P(not red)
5/8
P(red) + P(not red)
1
3/8 + 5/8 = 8/8 = 1
Pick a colour to chase. The brass slice is your event; the mustard slice is everything that isn't. Together they always fill the whole bar — so the two chances always add to 1.