3. A game at a school fete is played with a fair coin and a random number generator which generates random integers between 1 and 52 inclusive. It costs 50 pence to play the game. First, the player tosses the coin. If it lands on tails, the player loses. If it lands on heads, the player is allowed to generate a random number. If the number is 1 , the player wins \(\pounds 5\). If the number is between 2 and 13 inclusive, the player wins \(\pounds 1\). If the number is greater than 13 , the player loses.

1. Find the probability distribution of the player's profit.
2. Find the mean and standard deviation of the player's profit.
3. Given that 200 people play the game, calculate
   1. the expected number of players who win some money,
   2. the expected profit for the fete.