6 A box contains 3 red balls and 5 white balls. One ball is chosen at random from the box and is not returned to the box. A second ball is now chosen at random from the box.
- Find the probability that both balls chosen are red.
- Show that the probability that the balls chosen are of different colours is \(\frac { 15 } { 28 }\).
- Given that the second ball chosen is red, find the probability that the first ball chosen is red.
The random variable \(X\) denotes the number of red balls chosen. - Draw up the probability distribution table for \(X\).
- Find \(\operatorname { Var } ( X )\).