2025 CGSS PRELIMS P1 Q23

A bag contains 12 counters, \(n\) of which are green and the remainder are blue. One counter is drawn at random and not replaced.

1. Write down, in terms of \(n\), the probability that the counter is blue.[1]
2. A second counter is then drawn at random. Given that the probability that both counters drawn are blue is \(\dfrac5{22}\), form an equation in the form \(n^2+bn+c=0\), where \(b\) and \(c\) are integers.[3]