Question
There are two events, A and B. How do you mathematically determine whether events A and B are independent
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine whether two events \( A \) and \( B \) are independent, you use the definition of independence in probability theory. Specifically, events \( A \) and \( B \) are independent if and only if:
\[
P(A \cap B) = P(A) \cdot P(B)
\]
where:
- \( P(A) \) is the probability of event \( A \) occurring,
- \( P(B) \) is the probability of event \( B \) occurring,
- \( P(A \cap B) \) is the probability of both events \( A \) and \( B \) occurring simultaneously.
To test for independence, follow these steps:
1. Calculate \( P(A) \) and \( P(B) \).
2. Calculate \( P(A \cap B) \).
3. Compare \( P(A \cap B) \) with \( P(A) \cdot P(B) \).
If \( P(A \cap B) = P(A) \cdot P(B) \), then events \( A \) and \( B \) are independent. If not, they are dependent.
\[
P(A \cap B) = P(A) \cdot P(B)
\]
where:
- \( P(A) \) is the probability of event \( A \) occurring,
- \( P(B) \) is the probability of event \( B \) occurring,
- \( P(A \cap B) \) is the probability of both events \( A \) and \( B \) occurring simultaneously.
To test for independence, follow these steps:
1. Calculate \( P(A) \) and \( P(B) \).
2. Calculate \( P(A \cap B) \).
3. Compare \( P(A \cap B) \) with \( P(A) \cdot P(B) \).
If \( P(A \cap B) = P(A) \cdot P(B) \), then events \( A \) and \( B \) are independent. If not, they are dependent.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.