Suppose that events E and F are​ independent, ​P(E)=0.6 and ​P(F)=0.6. What is the P(E and F)​?

Since events \( E \) and \( F \) are independent, the probability of both events occurring (i.e., \( P(E \text{ and } F) \)) is the product of their individual probabilities:

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

Given:
- \( P(E) = 0.6 \)
- \( P(F) = 0.6 \)

Thus:

\[
P(E \text{ and } F) = 0.6 \times 0.6 = 0.36
\]

Therefore, \( P(E \text{ and } F) = 0.36 \).

Would you like more details or further explanations on this topic?

Here are 5 related questions to expand on this:

1. What is the probability of \( P(E \text{ or } F) \) if events \( E \) and \( F \) are independent?
2. How does the concept of independent events differ from mutually exclusive events?
3. What would happen to \( P(E \text{ and } F) \) if \( P(E) \) were 0.8 and \( P(F) \) were 0.5?
4. How do you calculate the conditional probability \( P(E \mid F) \) for independent events?
5. How can you determine if two events are independent given probabilities?

**Tip:** For independent events, knowing one event occurs does not affect the likelihood of the other event happening.

Learn how to calculate the probability of two independent events occurring together using the formula P(E and F) = P(E) * P(F). In this problem, P(E)=0.6 and P(F)=0.6, resulting in a solution of P(E and F) = 0.36. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation