Here's the whole idea in one sentence: once you've picked an event, everything else that could happen is its complement — and between them they cover the lot.
The Event and Its "everything Else"
Reach into the bag in the toy and chase red. Some balls are red — that's your event. Every other ball, gold or green, is "not red" — that's the complement. There's no third option: a ball is either red or it isn't. So if you shade the red slice and the not-red slice, together they fill the entire bar, because every single ball is in one slice or the other.
Why the Chances Add to 1
Probability is favourable ÷ total, and the whole bag is the total. If 3 of 8 balls are red, then P(red) is 3/8. The other 5 are not red, so P(not red) is 5/8. Add them: 3/8 + 5/8 = 8/8 = 1. It can't be anything else — the favourable counts for "is" and "isn't" must add up to the total, because that's literally every ball. Change the bag with "new bag" and watch the two fractions shift, but the sum stays glued to 1.
Why That Matters
That stuck-at-1 fact is the engine for the whole concept. If the two chances always add to 1, then knowing one hands you the other for free — no recounting needed. That's the shortcut you'll meet next rung, and it's what turns nasty "at least one" questions into easy ones later on.