The Probabilistic Method

Proving a structure exists by showing a random one works, sharpened by the moment methods, by deletion, and by the Lovász Local Lemma.0/10 mastered

1 / 10

In the hypothesis

\Pr[A_i] \le x_i\prod_{j\in N(i)}(1-x_j)

, suppose

x_i = 1/4

for all

i

and

A_i

has exactly two neighbours. What is the largest probability

\Pr[A_i]

allowed?

Your answer

#13169