1 In a game at a charity fair, a spinner is spun 4 times.
On each spin the chance that the spinner lands on a score of 5 is 0.2 .
The random variable \(X\) represents the number of spins on which the spinner lands on a score of 5 .

1. Find \(\mathrm { P } ( X = 3 )\).
2. Find each of the following.
   • \(\mathrm { E } ( X )\)
   • \(\operatorname { Var } ( X )\)
   One game costs \(\pounds 1\) to play and, for each spin that lands on a score of 5 , the player receives 50 pence.
3. 1. Find the expected total amount of money gained by a player in one game.
   2. Find the standard deviation of the total amount of money gained by a player in one game.