I'd advice you to avoid choosing examples, which might have a different perceived probability than the real one in most people - the usual example would be things which often get reported on the news (which leads to them being are perceived as more likely than they are). Alternatively, use those examples but only in conjunction with other [hopefully] less distorted ones.

I'd personally mostly use examples that relate to sports, games and so on - e.g. chance to draw 2 aces in a row from a pack of cards.