Fact Check: Are events independent?

Fact Check: Are events independent?

Published May 8, 2025
VERDICT
True

# Are Events Independent? ## Introduction The claim in question revolves around the concept of independence in probability theory, specifically askin...

Are Events Independent?

Introduction

The claim in question revolves around the concept of independence in probability theory, specifically asking whether events can be classified as independent. In statistical terms, two events are considered independent if the occurrence of one does not influence the probability of the occurrence of the other. This claim is fundamental to various applications in statistics, data analysis, and risk assessment.

What We Know

  1. Definition of Independence: According to probability theory, two events A and B are independent if knowing that A has occurred does not change the probability of B occurring. This can be mathematically expressed as P(B|A) = P(B) 12.

  2. Mutual Exclusivity vs. Independence: It is important to distinguish between independent events and mutually exclusive events. Mutually exclusive events cannot occur at the same time, while independent events can occur simultaneously without affecting each other's probabilities 45.

  3. Examples of Independent Events: Common examples include flipping a coin and rolling a die. The outcome of one does not affect the outcome of the other, making them independent events 9.

  4. Mathematical Representation: The independence of two events can also be expressed in terms of their joint probability: events A and B are independent if P(A ∩ B) = P(A) * P(B) 10.

  5. Importance in Statistical Analysis: Understanding the independence of events is crucial for building probabilistic models and making statistical inferences. It simplifies the calculations involved in probability theory and helps in risk assessment 79.

Analysis

The sources cited provide a range of definitions and explanations regarding the independence of events in probability theory.

  • Wikipedia is a widely used source, but its reliability can vary depending on the contributors. While it offers a comprehensive overview of the concept, it is essential to cross-reference with more specialized academic sources 1.

  • Academic Institutions: The source from Berkeley provides a more rigorous academic perspective on independence, which is beneficial for understanding the mathematical foundations of the concept 2. However, it is essential to consider that educational materials may sometimes simplify complex topics for teaching purposes.

  • Khan Academy is known for its educational content aimed at students, which can be reliable for foundational understanding but may lack depth for advanced inquiries 3.

  • GeeksforGeeks offers explanations that are accessible but may not always be peer-reviewed, raising questions about the depth of their content 45.

  • Byju's and Math is Fun are educational platforms that provide simplified explanations, which can be helpful for beginners but may not delve into the complexities of the topic 68.

  • Electra Radioti's article appears to be a more specialized source that discusses the importance of independence in statistical modeling, which could provide valuable insights but should be evaluated for potential bias given its less well-known origin 7.

  • Stack Exchange provides a platform for discussions among mathematicians and statisticians, which can yield valuable insights but may also include unverified claims or opinions that require careful scrutiny 10.

Methodological Concerns

While the definitions and examples provided by these sources are generally consistent, the methodology behind how independence is determined can vary. For instance, some sources may present independence in a purely theoretical context, while others may include practical applications. Additional empirical studies or case analyses would strengthen the understanding of how independence manifests in real-world scenarios.

Conclusion

Verdict: True

The claim that events can be classified as independent is supported by a robust framework in probability theory. Key evidence includes the mathematical definitions of independence, which state that two events A and B are independent if the occurrence of one does not affect the probability of the other, as expressed by P(B|A) = P(B) and P(A ∩ B) = P(A) * P(B). Numerous examples, such as flipping a coin and rolling a die, further illustrate this concept.

However, it is essential to recognize that while the theoretical framework is well-established, the application of these principles can vary in practice. The sources reviewed provide a mix of foundational knowledge and practical examples, but some may lack depth or peer review, which could affect the reliability of their claims.

Readers should be aware that while the concept of independence is widely accepted in probability theory, the nuances of its application in real-world scenarios may require further empirical investigation. As always, it is advisable for readers to critically evaluate information and consult multiple sources when forming conclusions.

Sources

  1. Independence (probability theory) - Wikipedia. Link
  2. Events A and B are independent if: knowing whether A ... - Berkeley. Link
  3. Conditional probability and independence - Khan Academy. Link
  4. Mutually Exclusive Events vs Independent Events - GeeksforGeeks. Link
  5. Dependent and Independent Events | GeeksforGeeks. Link
  6. Independent Events And Probability - Byju's. Link
  7. Independence of Events in Probability Theory - Electra Radioti. Link
  8. Probability: Independent Events - Math is Fun. Link
  9. Independent Events: Probability & Examples - Science Insider. Link
  10. Confusion about Independent events - Mathematics Stack Exchange. Link

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Fact Check: Autistic Non-Verbal Episodes in Marriage: Why Words Vanish Sometimes and What to Do About It Neurodiverse Couples Tuesday, august 12, 2025. Here’s the scene: You’re in the middle of a conversation with your spouse. Maybe the topic is small (“Did you pay the water bill?”) or monumental (“Are we happy?”). And then—without warning—your autistic partner’s voice disappears. No yelling, no slammed doors. Just… gone. You’re left holding the conversational steering wheel while they’ve quietly climbed into the trunk. If you’ve never lived with high-functioning autism, this can be tragically misconstrued as stonewalling or contempt. It isn’t. It’s just neurology pulling the emergency brake. Why This Happens: The Science Without the Lab Coat Smell For autistic adults, losing speech under stress is often a shutdown—a form of nervous system overload that knocks language production offline. Think of it like your phone freezing: all the apps are still there, but none of them open when you tap. Research calls this autistic burnout when it happens in a longer, chronic cycle—linked to masking (Hull et al., 2017; Raymaker et al., 2020). Masking is the art of “performing normal” so well that non-autistic people think you’re fine. The issue is that it eats through your energy reserves like a car idling in traffic with the A/C on full blast (Mantzalas et al., 2022). Eventually, one hard conversation can tip you from functional to frozen. And here’s where couples therapy meets neuroscience: physiological flooding—the body’s fight/flight/freeze switch—is a known relationship killer (Malik et al., 2019; Gottman Institute, 2024). In other words, for some autistic partners, flooding may tend to show up sooner, last longer, and is more likely to pull the plug on speech entirely. The Danger Loop in Marriage Autistic partner goes non-verbal — brain says “nope.” Non-autistic partner reads it as avoidance — brain says “attack.” Pressure increases — “Just say something.” Shutdown deepens — and now you’ve both lost. Do that a few hundred times and you’ll start conflating a physiological response into a moral failing. That’s the real marriage-killer. The Protocol: Three Phases, Zero Guesswork This is where we get practical. You can’t “love away” a temporary shutdown, but you can stop it from turning into World War III. Before: Build the Net Name the state. Agree on a phrase or signal ( I call this a couple code)—such as “words offline,” “shutdown,” a hand over the heart. The point is to make the invisible visible. The Shutdown Card. A literal card that says: I can’t speak right now. Please lower lights, reduce sound, give me X minutes. I promise I will circle back. The Pause Rule. Require a minimum of 20 minutes before resuming any tough talk. Autistic partner may need 90+. Agree ahead of time. Downgrade Kit. the usual gear; earplugs, soft light, weighted blanket, fidget, a quiet room. You know, human decency in object form. Reduce Daily Load. Avoid heavy talks right after work or big social events. Chronic overload makes a nervous shutdown more probable. During: Do Less, Better Autistic Partner: Give the signal. Exit stimulation. Switch channels if possible (text, notes app, yes/no cards). Send a short pre-written message: “Safe, can’t talk, back at 8:15.” Non-Autistic Partner: Acknowledge once—“Got it, I’m with you.” Hold the pause boundary. Lower stimuli. Go regulate your own nervous system—walk, journal, pet the dog. Don’t rehearse comebacks. Both: Avoid sarcasm, interrogation, ultimatums. Nothing lengthens a shutdown like moral outrage. After: Close the Loop Check in: “Are you ready to talk, or should we start in text?” Debrief: Identify triggers and what helped. Solve the actual problem. 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F., et al. (2023). The lived experience of meltdowns for autistic adults. Autism, 27(7), 1787–1799. https://doi.org/10.1177/13623613221145783 Malik, J., et al. (2019). Emotional flooding in response to negative affect in romantic relationships. Journal of Couple & Relationship Therapy, 18(4), 327–349. https://doi.org/10.1080/15332691.2019.1641188 Gottman Institute. (2024, March 4). Making sure emotional flooding doesn’t capsize your relationship. Retrieved from https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/

Detailed fact-check analysis of: Autistic Non-Verbal Episodes in Marriage: Why Words Vanish Sometimes and What to Do About It Neurodiverse Couples Tuesday, august 12, 2025. Here’s the scene: You’re in the middle of a conversation with your spouse. Maybe the topic is small (“Did you pay the water bill?”) or monumental (“Are we happy?”). And then—without warning—your autistic partner’s voice disappears. No yelling, no slammed doors. Just… gone. You’re left holding the conversational steering wheel while they’ve quietly climbed into the trunk. If you’ve never lived with high-functioning autism, this can be tragically misconstrued as stonewalling or contempt. It isn’t. It’s just neurology pulling the emergency brake. Why This Happens: The Science Without the Lab Coat Smell For autistic adults, losing speech under stress is often a shutdown—a form of nervous system overload that knocks language production offline. Think of it like your phone freezing: all the apps are still there, but none of them open when you tap. Research calls this autistic burnout when it happens in a longer, chronic cycle—linked to masking (Hull et al., 2017; Raymaker et al., 2020). Masking is the art of “performing normal” so well that non-autistic people think you’re fine. The issue is that it eats through your energy reserves like a car idling in traffic with the A/C on full blast (Mantzalas et al., 2022). Eventually, one hard conversation can tip you from functional to frozen. And here’s where couples therapy meets neuroscience: physiological flooding—the body’s fight/flight/freeze switch—is a known relationship killer (Malik et al., 2019; Gottman Institute, 2024). In other words, for some autistic partners, flooding may tend to show up sooner, last longer, and is more likely to pull the plug on speech entirely. The Danger Loop in Marriage Autistic partner goes non-verbal — brain says “nope.” Non-autistic partner reads it as avoidance — brain says “attack.” Pressure increases — “Just say something.” Shutdown deepens — and now you’ve both lost. Do that a few hundred times and you’ll start conflating a physiological response into a moral failing. That’s the real marriage-killer. The Protocol: Three Phases, Zero Guesswork This is where we get practical. You can’t “love away” a temporary shutdown, but you can stop it from turning into World War III. Before: Build the Net Name the state. Agree on a phrase or signal ( I call this a couple code)—such as “words offline,” “shutdown,” a hand over the heart. The point is to make the invisible visible. The Shutdown Card. A literal card that says: I can’t speak right now. Please lower lights, reduce sound, give me X minutes. I promise I will circle back. The Pause Rule. Require a minimum of 20 minutes before resuming any tough talk. Autistic partner may need 90+. Agree ahead of time. Downgrade Kit. the usual gear; earplugs, soft light, weighted blanket, fidget, a quiet room. You know, human decency in object form. Reduce Daily Load. Avoid heavy talks right after work or big social events. Chronic overload makes a nervous shutdown more probable. During: Do Less, Better Autistic Partner: Give the signal. Exit stimulation. Switch channels if possible (text, notes app, yes/no cards). Send a short pre-written message: “Safe, can’t talk, back at 8:15.” Non-Autistic Partner: Acknowledge once—“Got it, I’m with you.” Hold the pause boundary. Lower stimuli. Go regulate your own nervous system—walk, journal, pet the dog. Don’t rehearse comebacks. Both: Avoid sarcasm, interrogation, ultimatums. Nothing lengthens a shutdown like moral outrage. After: Close the Loop Check in: “Are you ready to talk, or should we start in text?” Debrief: Identify triggers and what helped. Solve the actual problem. No conflict gets left to rot in the corner. Spot burnout early. If shutdowns start clustering, it’s time to reduce demands, not double them. How This Isn’t Stonewalling Stonewalling is a choice. Shutdown is a lockout. Stonewalling says, “I won’t talk to you.” Shutdown says, “I can’t talk to you yet, but I will.” The key difference? Repair intention. A shutdown protocol builds that right into the process. The Ten-Minute At-Home Drill Co-create your signal and card. Agree on a pause window. Pack the downgrade kit. Rehearse the exchange (“Got it, I’m with you.”). Check in weekly to tweak the system. Remember, you’re not aiming for zero shutdowns. You’re aiming for shorter, kinder, safer ones. Why This Works Because it matches lived autistic experience (Raymaker et al., 2020; Lewis et al., 2023). Because it honors nervous system limits instead of punishing them (Malik et al., 2019). Because it lets both partners keep their dignity and still solve the problem. 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F., et al. (2023). The lived experience of meltdowns for autistic adults. Autism, 27(7), 1787–1799. https://doi.org/10.1177/13623613221145783 Malik, J., et al. (2019). Emotional flooding in response to negative affect in romantic relationships. Journal of Couple & Relationship Therapy, 18(4), 327–349. https://doi.org/10.1080/15332691.2019.1641188 Gottman Institute. (2024, March 4). Making sure emotional flooding doesn’t capsize your relationship. Retrieved from https://www.gottman.com/blog/making-sure-emotional-flooding-doesnt-capsize-your-relationship/

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