Question 2 A bag contains 4 red balls, 3 black balls, and 3 green balls. Two balls are randomly drawn from the bag one after the other with replacement. 2.1 Construct a tree diagram to represent all possible outcomes of drawing two balls in succession. Clearly label the branches with the corresponding probabilities.

A tree diagram for this scenario will have two levels, representing the first and second draw: 1. **First Draw:** The probability of drawing a red ball (R) is 4/10, black ball (B) is 3/10, and green ball (G) is 3/10. Label the branches with these probabilities: - R (4/10) - B (3/10) - G (3/10) 2. **Second Draw:** Because the draws are made with replacement, the probabilities remain the same for the second draw. - From R: R (4/10), B (3/10), G (3/10) - From B: R (4/10), B (3/10), G (3/10) - From G: R (4/10), B (3/10), G (3/10) Each potential outcome can be represented at the end of each branch. For example, if you first draw R and then R again, the path would be R → R. But wait! This is just a glimpse into probability. Did you know that tree diagrams can also help in decision-making or project planning? They visually break down complex processes, making them easier to analyze. And if you're looking for common pitfalls, be careful when multiplying probabilities along the branches. Some might mistakenly think they need to add them, but multiplication is key here! Each path's probability is the product of the probabilities along that path. Fun fact: tree diagrams are not just for probability tasks; they can also be applied to genetics and even computer science for understanding hierarchical data structures!