To find $P(C_1 | B_2) \cdot P(B_2)$, we need to follow these steps:

1. Determine $P(C_1 | B_2)$, which is the probability of $C_1$ given $B_2$.
2. Determine $P(B_2)$, which is the probability of $B_2$.
3. Multiply these two probabilities.

From the tree diagram:

• $P(C_1 | B_2)$ is given directly by the branch from $B_2$ to $C_1$. This probability is $\frac{1}{4}$.
• $P(B_2)$ is given by the branch leading to $B_2$. This probability is also $\frac{1}{4}$.

Thus, $P(C_1 | B_2) = \frac{1}{4}$ and $P(B_2) = \frac{1}{4}$.

Now, multiply these probabilities: $P(C_1 | B_2) \cdot P(B_2) = \frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}$

So, the answer is $\frac{1}{16}$.

Would you like further details or have any questions about this solution?

Here are 5 numbered questions you might find helpful:

1. How do you find the total probability of an event in a tree diagram?
2. What is the difference between conditional probability and joint probability?
3. How can we use Bayes' Theorem with tree diagrams?
4. What are some common applications of probability tree diagrams?
5. How do we calculate the probability of independent events?

Tip: When working with tree diagrams, always start from the root and follow the branches to ensure you consider all possible outcomes.