Calculate variance given expectation

A question is this type if and only if it provides the expectation E(X) and asks to calculate Var(X) using the probability distribution.

1 questions · Standard +0.3

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CAIE S1 2014 June Q4
7 marks Standard +0.3
4 A book club sends 6 paperback and 2 hardback books to Mrs Hunt. She chooses 4 of these books at random to take with her on holiday. The random variable \(X\) represents the number of paperback books she chooses.
  1. Show that the probability that she chooses exactly 2 paperback books is \(\frac { 3 } { 14 }\).
  2. Draw up the probability distribution table for \(X\).
  3. You are given that \(\mathrm { E } ( X ) = 3\). Find \(\operatorname { Var } ( X )\).