The tree diagram represents a probability model where:

• Pen choices are Pink and Blue, with probabilities $\frac{7}{10}$ and $\frac{3}{10}$, respectively.
• Pencil choices after choosing a pen are Red and Green, with conditional probabilities $\frac{9}{10}$ and $\frac{1}{10}$, respectively, for each color.

Now, let’s calculate the probabilities for each outcome:

1. P, R (Pink, Red):
   Probability = $\frac{7}{10} \times \frac{9}{10} = \frac{63}{100}$

2. P, G (Pink, Green):
   Probability = $\frac{7}{10} \times \frac{1}{10} = \frac{7}{100}$

3. B, R (Blue, Red):
   Probability = $\frac{3}{10} \times \frac{9}{10} = \frac{27}{100}$

4. B, G (Blue, Green):
   Probability = $\frac{3}{10} \times \frac{1}{10} = \frac{3}{100}$

Now, we check that the total probability adds up to 1:

$\frac{63}{100} + \frac{7}{100} + \frac{27}{100} + \frac{3}{100} = \frac{100}{100} = 1$

This confirms our calculations are correct. Would you like any specific explanation or breakdown? Here are some further questions you might find interesting:

1. What is the probability of selecting a red pencil regardless of pen color?
2. What is the probability of choosing a green pencil?
3. How would the probabilities change if the pen probabilities were altered?
4. If you wanted the least likely outcome, which combination would that be?
5. How would these calculations differ with dependent events instead of independent?

Tip: Tree diagrams help visualize conditional probabilities clearly—practice with different branching scenarios for better understanding.