Estimate first

You flip a fair coin 100 times. What is the probability that you get exactly 50 heads?

Don't calculate — give your gut estimate.

%
Great intuition — it's about 8%. "Exactly 50" is the single most likely outcome, but it competes with 49, 51, 48, 52, … each almost as likely.
Lower than that — about 8%. Exactly 50 is the most likely single outcome, but it's just one of many plausible ones: 49, 51, 48, 52, … each nearly as likely.
Much lower — about 8%. "Fair coin" makes 50 feel inevitable, but exact equality is rare even when the coin is fair. You'll land between 40 and 60 about 95% of the time — just rarely on exactly 50.
Slightly higher — about 8%. You're right that it's small; 50 is still the single most likely count, it just shares probability with all its neighbors.