Suppose that E and F are two events and that P(E and F)equals=0.4 and P(E)equals=0.8 What is P(F|E)​?

The conditional probability \( P(F|E) \) is the probability of event \( F \) occurring given that event \( E \) has occurred. This is calculated using the formula:

\[
P(F|E) = \frac{P(E \cap F)}{P(E)}
\]

You are given:

- \( P(E \cap F) = 0.4 \)
- \( P(E) = 0.8 \)

Substitute the given values into the formula:

\[
P(F|E) = \frac{0.4}{0.8} = 0.5
\]

Therefore, \( P(F|E) = 0.5 \).

Would you like more details or have any further questions?

Here are some related questions:
1. What is the difference between conditional probability and joint probability?
2. How does Bayes' Theorem use conditional probability?
3. What happens to \( P(F|E) \) if \( P(E) = 0 \)?
4. Can \( P(F|E) \) ever exceed 1?
5. How do independent events affect conditional probabilities?

**Tip:** Conditional probabilities can help in understanding how events are dependent on one another.

Suppose that E and F are two events and that P(E and F) = 0.4 and P(E) = 0.8. What is P(F|E)?

Explore how to calculate conditional probability using the formula P(F|E) = P(E ∩ F) / P(E). This example involves P(E and F) = 0.4 and P(E) = 0.8. Perfect for students in Grades 9-12 studying probability theory and its applications.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation