5 Joanne has 10 identically-shaped discs, of which 1 is blue, 2 are green, 3 are yellow and 4 are red. She places the 10 discs in a bag and asks her friend David to play a game by selecting, at random and without replacement, two discs from the bag.

1. Show that:
   1. the probability that the two discs selected are the same colour is \(\frac { 2 } { 9 }\);
   2. the probability that exactly one of the two discs selected is blue is \(\frac { 1 } { 5 }\).
2. Using the discs, Joanne plays the game with David, under the following conditions: If the two discs selected by David are the same colour, she will pay him 135p. If exactly one of the two discs selected by David is blue, she will pay him 145p. Otherwise David will pay Joanne 45p.
   1. When a game is played, \(X\) is the amount, in pence, won by David. Construct the probability distribution for \(X\), in the form of a table.
   2. Show that \(\mathrm { E } ( X ) = 33\).
3. Joanne modifies the game so that the amount per game, \(Y\) pence, that she wins may be modelled by $$Y = 104 - 3 X$$
   1. Determine how much Joanne would expect to win if the game is played 100 times.
   2. Calculate the standard deviation of \(Y\), giving your answer to the nearest 1 p .