Probability of n events not happening
Source: Kürschak 2012, problem 3
July 6, 2014
probabilityexpected valuecombinatorics unsolvedcombinatorics
Problem Statement
Consider events, each of which has probability . We also know that the probability of any two both happening is . Prove the following.
(a) The probability that none of these events happen is at most .
(b) We can reach equality in (a) for infinitely many .