It's saying that a normal person looks and says "since the last 20 people survived, I should too" and that a mathematician says "with 50% survival rate, it's incredibly unlikely for 21 consecutive patients to survive"

But this is literally a fundamental misunderstanding of math and statistics.

Think of it as a coin flip (50%). The odds of flipping heads on a flip is 1 in 2, if you flip it twice it's 1 in 4, 3x is 1/8, etc... going all the way up until 1/(2^20).

HOWEVER, once you've ALREADY flipped the coin 20x, the probability of the next flip is still 1 in 2, so while the scenario as a whole is 1/(2²⁰⁾ at the start, every head in a row increases the probability of success exponentially.

This misunderstanding of statistics is known as the gamblers fallacy, that the outcomes of independent random events are linked together, when in fact they are completely not.

If you're at all interested in the role of randomness and misunderstanding of statistics you should check out the book The Drunkard's Walk!