How to determine if events are independent or dependent?
Understand the Problem
The question is asking how to assess whether two events are independent or dependent in probability theory. To determine this, we can use the definitions of independent and dependent events: two events A and B are independent if the occurrence of one does not affect the probability of the other. This can be tested using the formula P(A and B) = P(A) * P(B) for independence.
Answer
Compare P(A∩B) with P(A) * P(B) or check for changes in probability.
The final answer is to compare P(A∩B) with P(A) * P(B) or check if the probability of one event changes with the occurrence of the other.
Answer for screen readers
The final answer is to compare P(A∩B) with P(A) * P(B) or check if the probability of one event changes with the occurrence of the other.
More Information
Determining whether events are independent or dependent helps in calculating probabilities more accurately in scenarios where multiple events occur.
Tips
Common mistakes include forgetting to use the intersection probability (P(A∩B)) or not realizing when probabilities change.
Sources
- American Board guide on independent and dependent events - americanboard.org
- Lesson Explainer by Nagwa - nagwa.com
- Testing Independence on Math Stack Exchange - math.stackexchange.com
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