Three red balls and two blue balls are placed in a bag. All the balls are indistinguishable except f

Question

Three red balls and two blue balls are placed in a bag. All the balls are indistinguishable except for their colours.

Mr Red and Mr Blue take turns to draw a ball from the bag at random with replacement. The first player to draw the ball whose colour matches his name wins the game and the game stops immediately.

If Mr Red draws first, find the probability that

Mr Red wins the game at his third draw.[2]
Mr Blue wins the game at his ${{n}^{\mathrm{th}}}$ draw.[2]
Mr Red wins the game given that the winner wins the game at his third draw.[2]
Mr Blue wins the game.[2]

Accepted Answer

(i) $\frac{108}{3125}$ (ii) $\frac23\left(\frac6{25}\right)^n$ (iii) $\frac{15}{19}$ (iv) $\frac4{19}$

2015 AJC P2 Q9

2015 AJC P2 Q9

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