2013 DHS P2 Q7

A box contains \(5\) red balls, \(5\) green balls and \(5\) blue balls. The balls are identical in size. Balls of the same colour are each printed with a distinct number from \(1\), \(2\), \(3\), \(4\), \(5\). Two balls are randomly drawn without replacement. Find the probability that

1. at least \(1\) red ball is drawn,[2]
2. the sum of the numbers on the balls drawn is at least \(9\),[2]
3. the sum of the numbers on the balls drawn is at least \(9\) given that at least \(1\) red ball is drawn.[3]

State, with a reason, whether the events 'the sum of the numbers on the balls drawn is at least \(9\)' and 'at least \(1\) red ball is drawn' are independent.[1]