8 A game at a charity event uses a bag containing 19 white counters and 1 red counter. To play the game once a player takes counters at random from the bag, one at a time, without replacement. If the red counter is taken, the player wins a prize and the game ends. If not, the game ends when 3 white counters have been taken. Niko plays the game once.

1. (a) Copy and complete the tree diagram showing the probabilities for Niko. \section*{First counter} \includegraphics[max width=\textwidth, alt={}, center]{c985b9cc-a202-4d5d-a6b3-591b0560f570-4_293_426_1231_532}
   (b) Find the probability that Niko will win a prize.
2. The number of counters that Niko takes is denoted by \(X\).
   (a) Find \(\mathrm { P } ( X = 3 )\).
   (b) Find \(\mathrm { E } ( X )\).