Verify or show equation

A question is this type if and only if it asks to show, prove, or verify that a given equation or probability value is correct through calculation.

1 questions

CAIE S1 2020 November Q2
2 A bag contains 5 red balls and 3 blue balls. Sadie takes 3 balls at random from the bag, without replacement. The random variable \(X\) represents the number of red balls that she takes.
  1. Show that the probability that Sadie takes exactly 1 red ball is \(\frac { 15 } { 56 }\).
  2. Draw up the probability distribution table for \(X\).
  3. Given that \(\mathrm { E } ( X ) = \frac { 15 } { 8 }\), find \(\operatorname { Var } ( X )\).