4 Martin has won a competition. For his prize he is given six sealed envelopes, of which he is allowed to open exactly three and keep their contents. Three of the envelopes each contain \(\pounds 5\) and the other three each contain \(\pounds 1000\). Since the envelopes are identical on the outside, he chooses three of them at random. Let \(\pounds X\) be the total amount of money that he receives in prize money.

1. Show that \(\mathrm { P } ( X = 15 ) = 0.05\). The probability distribution of \(X\) is given in the table below.

   \(r\)	15	1010	2005	3000
   \(\mathrm { P } ( X = r )\)	0.05	0.45	0.45	0.05

2. Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).