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Fact Check: Are events independent?

Fact Check: Are events independent?

Published May 2, 2025
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# Are Events Independent? The claim in question revolves around the concept of independence in probability theory, specifically asking whether events...

Are Events Independent?

The claim in question revolves around the concept of independence in probability theory, specifically asking whether events can be classified as independent. This is a foundational topic in statistics and probability, with significant implications in various fields, including mathematics, finance, and science. The notion of independence suggests that the occurrence of one event does not influence the probability of another event occurring.

What We Know

  1. Definition of Independence: In probability theory, two events A and B are considered independent if the occurrence of A does not affect the probability of B occurring, mathematically expressed as P(B|A) = P(B) 13. This means that knowing whether A occurred provides no additional information about the likelihood of B.

  2. Examples of Independent Events: Common examples include flipping a coin and rolling a die. The outcome of the coin flip does not influence the outcome of the die roll, thus they are independent events 79.

  3. Dependent Events: In contrast, dependent events are those where the outcome of one event affects the outcome of another. For instance, drawing a card from a deck without replacement alters the probabilities of subsequent draws 49.

  4. Mathematical Representation: The probability of two independent events occurring together can be calculated by multiplying their individual probabilities: P(A and B) = P(A) * P(B) 89.

  5. Mutually Exclusive vs. Independent Events: It is crucial to differentiate between mutually exclusive events (which cannot occur at the same time) and independent events (which can occur simultaneously without affecting each other's probabilities) 6.

Analysis

The sources reviewed provide a comprehensive overview of the concept of independence in probability. However, the reliability and bias of these sources vary:

  • Wikipedia: While generally a good starting point for definitions and concepts, Wikipedia articles can be edited by anyone, which raises questions about the accuracy of specific content. The references used in the article should be checked for credibility 1.

  • NIST Computer Security Resource Center: As a government website, this source is likely to be reliable and objective, providing a clear definition of statistically independent events 2. However, it focuses more on applications in computer security rather than broader statistical theory.

  • Educational Institutions: The resource from the University of California, Berkeley, offers a detailed explanation of independence with mathematical rigor. Academic sources are typically reliable, but the complexity of the material may require a background in statistics for full comprehension 3.

  • GeeksforGeeks and BYJU'S: These platforms provide educational content, but they may cater to a specific audience, which could influence the depth and rigor of their explanations. They are generally reliable but should be cross-referenced with academic sources for critical concepts 45.

  • Math is Fun and Khan Academy: These sources are designed for educational purposes and are user-friendly, making complex topics accessible. They are generally reliable but may simplify concepts to aid understanding, which can lead to oversights in nuance 710.

Potential Conflicts of Interest

Some sources, particularly those aimed at educational purposes, may have a vested interest in promoting certain methodologies or concepts, which could introduce bias. For example, platforms like BYJU'S may prioritize content that aligns with their educational products.

Methodological Concerns

The claim regarding the independence of events is well-supported by mathematical principles; however, the application of these principles can vary based on context. For example, in real-world scenarios, determining independence may require extensive data analysis and consideration of external factors that could influence outcomes.

Conclusion

Verdict: True

The evidence reviewed supports the claim that events can be classified as independent in probability theory. The mathematical definitions and examples provided illustrate that the occurrence of one event does not affect the probability of another event occurring, which is the essence of independence.

However, it is important to note that while the theoretical framework is robust, real-world applications may introduce complexities that challenge the straightforward classification of events as independent. Factors such as external influences and the context of the events can complicate this determination.

Moreover, the reliability of the sources varies, and while many are credible, some may have biases or limitations that could affect the interpretation of independence. Therefore, while the conclusion is supported by sound mathematical principles, readers should remain cautious and critically evaluate the context in which independence is applied.

As always, it is advisable for readers to engage with the material critically and consider multiple perspectives when evaluating claims related to probability and statistics.

Sources

  1. Independence (probability theory) - Wikipedia. https://en.wikipedia.org/wiki/Independence_(probability_theory)
  2. Statistically Independent Events - Glossary | CSRC. https://csrc.nist.gov/glossary/term/statistically_independent_events#:~:text=Two%20events%20are%20independent%20if,%2C%20P(A%20and%20B)
  3. Events A and B are independent if: knowing whether A ... https://www.stat.berkeley.edu/~aldous/134/lecture3.pdf
  4. Dependent and Independent Events | GeeksforGeeks. https://www.geeksforgeeks.org/dependent-and-independent-events-probability/
  5. Independent Events And Probability - BYJU'S. https://byjus.com/maths/independent-events/
  6. Mutually Exclusive Events vs Independent Events - GeeksforGeeks. https://www.geeksforgeeks.org/mutually-exclusive-events-vs-independent-events/
  7. Probability: Independent Events - Math is Fun. https://www.mathsisfun.com/data/probability-events-independent.html
  8. Independence of Events in Probability Theory - Electra Radioti. https://electraradioti.com/statistics-and-probability/independence-of-events-in-probability-theory/
  9. Dependent Events and Independent Events - Statistics How To. https://www.statisticshowto.com/probability-and-statistics/dependent-events-independent/
  10. Conditional probability and independence (article) - Khan Academy. https://www.khanacademy.org/math/ap-statistics/probability-ap/stats-conditional-probability/a/check-independence-conditional-probability

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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. 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. In other words: you’re building a marriage that can survive the occasional moments when the words are gone for the time being. Be Well, Stay Kind, and Godspeed. REFERENCES: Hull, L., Mandy, W., Lai, M.-C., Baron-Cohen, S., Allison, C., Smith, P., & Petrides, K. V. (2017). “Putting on my best normal”: Social camouflaging in adults with autism spectrum conditions. Autism, 21(5), 611–622. https://doi.org/10.1177/1362361316671012 Raymaker, D. M., Teo, A. R., Steckler, N. A., Lentz, B., Scharer, M., Delos Santos, A., … & Nicolaidis, C. (2020). “Having all of your internal resources exhausted beyond measure and being left with no clean-up crew”: Defining autistic burnout. Autism in Adulthood, 2(2), 132–143. https://doi.org/10.1089/aut.2019.0079 Mantzalas, J., Richdale, A. L., Adikari, A., Lowe, J., & Dissanayake, C. (2022). What Is Autistic Burnout? A thematic analysis of posts on two online platforms. Autism in Adulthood, 4(1), 52–65. https://doi.org/10.1089/aut.2021.0079 Lewis, L. 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. In other words: you’re building a marriage that can survive the occasional moments when the words are gone for the time being. Be Well, Stay Kind, and Godspeed. REFERENCES: Hull, L., Mandy, W., Lai, M.-C., Baron-Cohen, S., Allison, C., Smith, P., & Petrides, K. V. (2017). “Putting on my best normal”: Social camouflaging in adults with autism spectrum conditions. Autism, 21(5), 611–622. https://doi.org/10.1177/1362361316671012 Raymaker, D. M., Teo, A. R., Steckler, N. A., Lentz, B., Scharer, M., Delos Santos, A., … & Nicolaidis, C. (2020). “Having all of your internal resources exhausted beyond measure and being left with no clean-up crew”: Defining autistic burnout. Autism in Adulthood, 2(2), 132–143. https://doi.org/10.1089/aut.2019.0079 Mantzalas, J., Richdale, A. L., Adikari, A., Lowe, J., & Dissanayake, C. (2022). What Is Autistic Burnout? A thematic analysis of posts on two online platforms. Autism in Adulthood, 4(1), 52–65. https://doi.org/10.1089/aut.2021.0079 Lewis, L. 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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