Brain Teasers

Hard brain teasers are where probability shows up. The waiting-time paradox, the birthday problem, and classic rate puzzles where your intuition actively fights against the correct answer. These are genuinely hard, not just tricky.

For probability teasers: if you're not sure, try to simulate it. Even mentally running through 10 cases often reveals whether the "obvious" answer holds up. For rate problems: always convert to the same units before combining. Most mistakes come from mixing hours and minutes or forgetting to account for overlap.