Find 
P(C1|B2) · P(B2).
 (Enter your answer as a fraction.)

We have already calculated the necessary probabilities from the tree diagram.

From the tree diagram:
- \( P(C_1 | B_2) = \frac{1}{4} \)
- \( P(B_2) = \frac{1}{4} \)

So, we need to find:
\[ P(C_1 | B_2) \cdot P(B_2) \]

\[ P(C_1 | B_2) \cdot P(B_2) = \frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16} \]

Therefore, 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:** Always ensure to multiply probabilities along the paths in the tree diagram to find joint probabilities.

Learn how to calculate the joint probability P(C1|B2) · P(B2) using conditional probability. This problem involves applying probability concepts to find the product of conditional and unconditional probabilities.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation