A bag contains $4$ black balls and $6$ white balls. Three balls are drawn from the bag at random

Question

A bag contains $4$ black balls and $6$ white balls. Three balls are drawn from the bag at random, one by one. If a black ball is drawn, it is replaced in the bag. If a white ball is drawn, it is not replaced and $2$ extra black balls are added to the bag. Show that the probability that all balls drawn are white is $\frac{1}{11}$.[2] Given that at least one of the balls drawn is black, find the probability that all balls drawn are black.[3] A fourth ball is further drawn from the bag at random. Find the probability that the third white ball appears on this fourth draw.[3]

Accepted Answer

(i) $\frac1{11}$ (ii) $\frac{44}{625}$ (iii) $\frac{266}{1815}$

2013 JJC P2 Q9

2013 JJC P2 Q9

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