1. Leofranc is playing a gambling game with a fair six-sided dice on which the faces are numbered 1 to 6.  He must pay £2 to play the game.  He then chooses a ‘lucky number’ between 1 and 6, and rolls the dice until either his lucky number appears or he has rolled the dice four times.  If his lucky number appears on the first roll, he receives £5 back.  If his lucky number appears on the second, third or fourth rolls, he receives £3, £2 or £1 back respectively.  If his lucky number has not appeared by the fourth roll, then the game is over and he receives nothing back.

 The random variable $W$ is defined to be Leofranc’s profit (i.e., the amount of money he receives back minus the cost of playing the game) when he plays the game one time.  Note that a negative profit indicates that Leofranc has lost money on the game.

Write down the probability distribution of $W$ in table form.