2025 RVHS P2 Q8

A game at a funfair involves pulling balls of different colours out of a bag. A bag contains \(1\) white ball, \(2\) blue balls, \(3\) green balls and \(4\) red balls. The aim of the game is to pull the white ball from the bag as many times as possible. Players get three attempts. If a red ball is drawn, it is discarded, but any other ball is replaced in the bag.

1. Find the probability that a player draws a white ball and two green balls on their three attempts.[2]
2. Find the probability that exactly one white ball was drawn, given that a red ball was drawn on the second attempt.[3]

Events \(A\) and \(B\) are defined as

\(A\): A white ball is drawn on the first attempt
\(B\): A white ball is drawn on the second attempt

3. Determine with reason whether events \(A\) and \(B\) are independent.[2]