Suppose that E and F are two events and that Upper P left parenthesis Upper E and Upper F right parenthesisequals0.5 and Upper P left parenthesis Upper E right parenthesisequals0.8. What is Upper P left parenthesis F|E right parenthesis​?
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Part 1
Upper P left parenthesis F|E right parenthesisequals
  
enter your response here ​(Type an integer or a decimal. Do not​ round.)

To find \( P(F|E) \), we can use the formula for conditional probability:

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

Given:
- \( P(E \text{ and } F) = 0.5 \)
- \( P(E) = 0.8 \)

Now, substitute these values into the formula:

\[
P(F|E) = \frac{0.5}{0.8} = 0.625
\]

So, \( P(F|E) = 0.625 \).

Would you like a more detailed explanation, or do you have any questions?

Here are 5 related questions you might find useful:
1. What is the formula for the conditional probability of two events?
2. How would you calculate \( P(E|F) \) if \( P(F) \) is also given?
3. What does it mean if \( P(F|E) = 1 \)?
4. Can \( P(E \text{ and } F) \) ever be greater than \( P(E) \) or \( P(F) \)?
5. How does independence of events \( E \) and \( F \) affect \( P(F|E) \)?

**Tip:** Understanding the relationship between joint probability and conditional probability is crucial for solving problems involving dependent events.

Learn how to calculate conditional probability P(F|E) with a detailed explanation and step-by-step solution. Given P(E and F) = 0.5 and P(E) = 0.8, find P(F|E) using the conditional probability formula. Suitable for high school students.

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