Probability: Picking a Ball from a Bag

A ball is selected at random from a bag. The bag contains \(30\) balls of which \(8\) balls are blue, \(x\) balls are red and the rest are purple.

1. Find the probability of selecting
   1. a blue ball,
   2. a black ball.
2. If the probability of picking a purple ball is \(\frac{1}{5}\), find the value of \(x\).