It seems you mentioned a tree diagram and related conditional probabilities, but I don't have access to a diagram directly from your input. If you could upload the tree diagram or provide the relevant probabilities and structure (such as the branches, outcomes, and probabilities of each event), I can guide you through calculating $P(A | E)$ and $P(C | F)$.

In conditional probability, we use the following formulas:

• $P(A | E) = \frac{P(A \cap E)}{P(E)}$
• $P(C | F) = \frac{P(C \cap F)}{P(F)}$

Where:

• $P(A \cap E)$ is the joint probability that both $A$ and $E$ occur.
• $P(C \cap F)$ is the joint probability that both $C$ and $F$ occur.
• $P(E)$ and $P(F)$ are the marginal probabilities of $E$ and $F$, respectively.

Let me know if you can provide more details or upload the diagram so I can help you solve this!

Do you want more details or examples to clarify this?

Here are 5 related questions:

1. How do you calculate the marginal probability $P(E)$ from a tree diagram?
2. What is the difference between joint and conditional probabilities in tree diagrams?
3. How does Bayes' Theorem relate to conditional probability?
4. What does it mean when two events are independent in terms of conditional probability?
5. How can you calculate total probability from multiple branches in a tree diagram?

Tip: In tree diagrams, always start by identifying the paths that lead to the events you're interested in, then use those paths to calculate probabilities.