Seven red counters and two blue counters are placed in a bag. All the counters are indistinguishable

Question

Seven red counters and two blue counters are placed in a bag. All the counters are indistinguishable except for their colours. Clark and Kara take turns to draw a counter from the bag at random with replacement. The first player to draw a blue counter wins the game and the game ends immediately.

If Clark draws first, find the probability that

Clark wins the game at his third draw,[2]
Kara wins the game.[3]

Accepted Answer

(i) $0.0813$ (ii) $\frac7{16}$

2017 IJC P2 Q6

2017 IJC P2 Q6

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