A bag contains four red and eight blue balls of which two of the red balls and six of the blue balls

Question

A bag contains four red and eight blue balls of which two of the red balls and six of the blue balls have the number "$0$" printed on them. The remaining balls have the number "$1$" printed on them. Three balls are randomly drawn from the bag without replacement.

Show that the probability that at least one blue ball is drawn is $\frac{54}{55}$.[1]

Find the probability that

at least one ball of each colour is drawn,[2]
the sum of the numbers on the balls drawn is at least two.[3]

Accepted Answer

(i) $\dfrac{54}{55}$ (ii) $\dfrac8{11}$ (iii) $\dfrac{13}{55}$

2016 CJC P2 Q5

2016 CJC P2 Q5

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