Bag contains n marbles, two of which are blue. Hayley plays a game in which she randomly draws marbles out of the bag, one after another, without replacement. The game ends when Hayley draws a blue marble. (a) [1 mark] Find the probability, in terms of n, that the game will end in her first draw.

(b) [3 marks] Find the probability, in terms of n, that the game will end on her second draw.

(c) [2 marks] Let n=5
n
=
5
. Find the probability that the game will end on her third draw.

(d) [2 marks] Let n=5
n
=
5
. Find the probability that the game will end on her fourth draw.

Hayley plays the game when n=5
n
=
5
. She pays $20 to play and can earn money back depending on the number of draws it takes to obtain a blue marble. She earns no money back if she obtains a blue marble on her first draw. Let M be the amount of money that she earns back playing the game. This information is shown in the following table.