2012 HCI P2 Q8

An eatery is giving out free burgers in a promotion to celebrate its anniversary. A total of \(80\) burgers, consisting of \(8\) different flavours, \(10\) from each flavour, are to be given out. The burgers are randomly chosen and given out one at a time. Of the \(8\) burger flavours, the ‘Curry’ and ‘Spicy’ burgers are most popular among customers. In the first four burgers to be given out, the events \(A\) and \(B\) are defined as follows:

\(A\): At least \(2\) ‘Curry’ burgers.

\(B\): Exactly one ‘Spicy’ burger.

1. Find \(\mathrm{P}\left( A|B \right)\).[3]
2. Justify if \(A'\) and \(B'\) are independent events.[3]