Your parents might tell you it's improbable that they'll buy you a car when you turn 16. Since improbable means something is unlikely but not impossible, your optimism allows you to keep hoping.
The adjective improbable also means statistically unlikely to happen. You might be afraid to fly, but the odds of a plane crash are so low that such an event is improbable. Improbable also means something that is so outrageous that you'd never admit you believed in it. You know the existence of the Loch Ness Monster is improbable, but that doesn't stop you from looking for it when you travel to Scotland.