1. 5
  1.  

  2. 3

    If stuff like this interests you, I would suggest reading about Concentration Inequalities [1][2]

    Concentration inequalities unify both of these inequalities and provide tools to make new ones for whatever situations you have.

    1. https://www.stat.berkeley.edu/~mjwain/stat210b/Chap2_TailBounds_Jan22_2015.pdf
    2. http://84.89.132.1/~lugosi/anu.pdf