https://file.aiquickdraw.com/mathbot/file/1730560254094drsq60mc.jpg

The problem on the image is asking for the conditional probability \( P(M|B) \), which means the probability of event \( M \) occurring given that event \( B \) has occurred.

### Step-by-Step Solution:

1. **Identify given data from the Venn diagram**:
   - The number in \( B \) only: \( 300 \)
   - The number in \( M \) only: \( 200 \)
   - The number in both \( B \) and \( M \) (the intersection of \( B \) and \( M \)): \( 50 \)
   - The total number of elements in the universal set (the entire box): \( 1000 \)

2. **Calculate the probability of \( B \) (event \( B \) occurring)**:
   \[
   P(B) = \frac{\text{Number in } B}{\text{Total number}} = \frac{300 + 50}{1000} = \frac{350}{1000} = 0.35
   \]

3. **Calculate the probability of both \( B \) and \( M \) (intersection)**:
   \[
   P(B \cap M) = \frac{\text{Number in both } B \text{ and } M}{\text{Total number}} = \frac{50}{1000} = 0.05
   \]

4. **Apply the formula for conditional probability**:
   \[
   P(M|B) = \frac{P(B \cap M)}{P(B)} = \frac{0.05}{0.35} \approx 0.14
   \]

### Answer:
The probability of \( M \) given \( B \) ( \( P(M|B) \) ) is approximately **0.14**.

Would you like further details on this solution?

---

Here are 5 related questions you might find interesting:
1. What is the probability of \( B \) given \( M \) ( \( P(B|M) \) ) using the same data?
2. How would you calculate the probability of \( M \) or \( B \) occurring?
3. What is the probability of neither \( M \) nor \( B \) occurring?
4. How does the interpretation of conditional probability change when there is no overlap between \( M \) and \( B \)?
5. Can we verify the total probability adds up to 1 using these values?

**Tip:** Conditional probability often depends on the overlap between events, which is visually represented in Venn diagrams for clarity.

What's the probability of M given B? Enter as a decimal to 2 places.

Explore a detailed solution to find the conditional probability P(M|B) using a Venn diagram with specific values. This example walks through identifying relevant areas and applying the conditional probability formula, ideal for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation