2024 RVHS H1 Q8

A box contains \(3\) blue balls and \(3\) red balls. Three balls are drawn from the box, one after another. If a blue ball is drawn, it is replaced in the box and another blue ball is added to the box before the next draw. If a red ball is drawn, it is not replaced and no ball is added. The following tree diagram illustrates all the possible outcomes from the first draw to the third draw, where \(B\) and \(R\) denotes the events that a blue and a red ball is drawn respectively.

1. Complete the tree diagram below.[2]

Tree diagram for ball selection

Find the probability that

2. none of the three balls drawn is red,[1]
3. exactly one of the three balls drawn is blue,[2]
4. the last ball drawn is blue, given that at least one of the three balls drawn is red.[4]