Section B ( 53 marks )
10 . A bag contains n marbles in which three of them are red and the rest of them are white . Phoebe plays a game in which she randomly draws marbles out of the bag one after another without replacement . The game ends when Phoebe draws a red marble .
( a ) Find the probability , in terms of n , that the game will end on her
( i ) first draw ;
( ii ) third draw .
( b ) Let n � 10 . Find the probability that the game will end on her fourth draw .
Phoebe plays the game when n � 10 . She pays $ 10 to play and can earn money back depending on the number of draws it takes to obtain a red marble . The table below shows the overall information :
[ 3 ]
[ 2 ]
Number of draws in total Money that Phoebe earns back
1 2 3 4 5 or above
10 10 25x 21x 0
( c ) Show that
2 x � if the game is fair .
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