2025 SJI PRELIMS P1 Q24

Bag A has 5 red and 3 blue balls. Bag B initially has \(x\) red and 2 blue balls. A ball is drawn from A and put into B; then a ball is drawn from B.

1. Draw a tree diagram showing the outcome probabilities.[2]
2. The probability of drawing red from A and then red from B is \(\dfrac5{12}\). Find \(x\).[2]
3. Explain how \(x\) affects the probability of drawing a blue ball from Bag B.[1]