Lesson 13

But what is the probability that you will not earn anything at all? This happens when there are at least two thousand winners, i.e., when the random variable “the number of winners” exceeds its expectation by at least a factor of two. Substituting \(\varepsilon=2\) into Chernoff's theorem, we get that this probability is at most \[e^{-t(2) \cdot 1000}=e^{-(0.386…)\cdot 1000}<e^{-386}\approx 2.30319 \cdot 10^{-168} .\] In practice, such a probability can, of course, be neglected!