Understanding Probability: Common Misconceptions Explained

Language and Probability

The Language of Probability: Clarity is Key.

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When someone states they are “probably” having pasta for dinner but later opts for pizza, do you find it surprising or consider them dishonest? On a more critical note, what does it imply when the United Nations asserts it is “very likely” that global temperatures will rise by over 1.5 degrees Celsius in the next decade, as reported last year? The translation between the nuances of language and the intricacies of mathematical probability can often seem challenging, yet we can discover scientific clarity through careful analysis.

Two fundamental points about probability are widely accepted: Something labeled “impossible” has a 0% chance of occurrence, while a “certain” event carries a 100% likelihood. However, confusion arises in between these extremes. Ancient Greeks, including Aristotle, differentiated between terms such as Eikos, meaning the most likely, and Pitanon, which signifies plausible. This presents challenges: persuasive rhetoric may not always align with likelihood. Additionally, both terms were translated by Cicero into the modern term probability.

The concept of a measurable mathematical approach to probability emerged significantly later, primarily in the mid-17th century during the Enlightenment. Mathematicians began to address gambling dilemmas, such as equitable distribution of winnings during interruptions. Concurrently, philosophers probed whether it was feasible to quantify varying levels of belief.

For instance, in 1690, John Locke categorized degrees of probability on a spectrum from complete certainty to confidence based on personal experience, down to testimony affected by repetition. This classification remains vital in legal contexts, both historically and presently.

The interplay between law and probability persisted among philosophers. In his writings of the mid-19th century, Jeremy Bentham criticized the inadequacy of common language in expressing evidence strength. He proposed a numerical ranking system to gauge belief strength, but ultimately deemed its subjectivity as impractical for justice.

A century later, economist John Maynard Keynes rejected Bentham’s certainty measure in favor of relational approaches. He argued that it was more effective to discuss how one probability might exceed another, focusing on the knowledge base for these estimations, thus establishing a hierarchy without offering systematic communication methods for terms such as “may” or “likely.”

Interestingly, the first systematic resolution to this challenge did not arise from mathematicians or philosophers but from a CIA intelligence analyst named Sherman Kent. In 1964, he introduced the idea of estimating probability with specific terminology for National Intelligence Estimates designed to guide policymakers. He articulated the dilemma faced by “poets,” who articulate meaning through words, versus “mathematicians,” who advocate for exact figures. Kent initiated the idea that specific words correspond to precise probabilities, designating “virtually certain” as a 93% probability, but also allowing some leeway to accommodate differing interpretations.

This framework for understanding probability transitioned from the intelligence sector to scientific applications. A review of recent research dating back to 1989 explored how both patients and medical professionals interpret terms like “may” in medical scenarios. The findings showed some alignment with Kent’s framework, although with distinctions.

Returning to the original question about the meaning of “very likely” regarding climate change, the Intergovernmental Panel on Climate Change (IPCC) offers clarity with explicit definitions. According to their guidance, “very likely” signifies a 90% to 100% probability of an event’s occurrence. Alarmingly, many climate scientists now assert that temperatures have already surpassed the critical threshold of 1.5 degrees Celsius.

However, situations are rarely straightforward. Logically, the statements “Event A is likely to occur” and “Event A is unlikely to be avoided” should correlate, albeit research published last year reveals that labeling a climate forecast as “unlikely” diminishes perceived evidence strength and consensus among scientists compared to stating it’s “likely.” This cognitive bias might stem from a preference for positive framing over negative alternatives. A classic example includes a community of 600 individuals facing a health crisis; when presented with two treatment options, most favor one that saves 200 lives over one that saves 400, even if both are statistically similar.

So, what lessons can we draw from this exploration? Firstly, quantifiable data effectively enhances communication of uncertainty. If numerical specificity isn’t available, stating, “75% of the time, I plan to have pasta for dinner,” may raise eyebrows. In such instances, ensure shared understanding of terminology, even in the absence of a formalized framework like Kent’s. Lastly, accentuating the positive tends to foster acceptance of predictions. How likely is that? Well, that’s hard to quantify.

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Source: www.newscientist.com

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Misconceptions about prostate cancer: What we need to know

Recent news about King Charles’ prostate issues and subsequent cancer diagnosis has raised awareness of such health issues nationwide. Although the king is not diagnosed with prostate cancer, his efforts to raise awareness among older men have been widely appreciated.

The charity Prostate UK is using billboards to encourage men across the country to assess their cancer risk and consult their GP if they experience symptoms like frequent or difficult urination. However, prostate cancer is a complex and subtle condition.


The prostate, located below the bladder, tends to enlarge with age. The urethra, the tube draining urine from the bladder to the outside, passes through it. When the prostate enlarges, it can put pressure on the urethra, causing symptoms like dribbling and increased frequency of urination. This condition is quite common.

Similarly, prostate cancer is also common. Autopsy studies show that 36% of whites and 51% of African Americans develop prostate cancer in their 70s. There are even cases of prostate cancer found in 5% of men under 30 in autopsy studies. However, not all forms of prostate cancer are equally dangerous, with some being harmless and others potentially fatal.

How dangerous is prostate cancer?

Prostate cancer accounts for around 4% of male deaths in the UK, with approximately 12,000 people dying from it each year. The challenge lies in finding treatments that do not cause further harm, as treatments like surgery and radiation therapy can lead to side effects such as erectile dysfunction and incontinence.

The lack of an accurate way to differentiate between aggressive and non-aggressive tumors is a major problem. The PSA test, developed in the 90s, was introduced to monitor men’s response to prostate cancer treatment. However, the increasing number of diagnoses did not correspond to a reduction in mortality rates.

In the US, the Preventive Services Task Force has offered recommendations for or against PSA screening. While screening may slightly reduce prostate cancer deaths, it can also lead to unnecessary testing and treatments for non-fatal conditions.

To avoid unnecessary treatment, the “watchful waiting” approach has been effective in managing localized prostate cancer with low mortality rates. In the UK, the National Screening Committee does not recommend PSA screening for prostate cancer.

Research suggests that identifying harmful cancers through prostate screening MRI scans may be a viable solution, although more evidence is needed to assess its impact on reducing deaths without overtreatment.


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Source: www.sciencefocus.com

Artificial Intelligence Will Not Eliminate Jobs, Despite Common Misconceptions.

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New research reveals that work experience has a significant impact on how employees interact with AI. Employees with more experience with a particular task will benefit more from AI, but senior employees will be less likely to trust her AI due to concerns about its imperfections. The findings highlight the need for customized strategies when integrating AI into the workplace to enhance human-AI teamwork.

New research sheds light on the complex aspects of human-AI interaction and reveals some surprising trends. Artificial intelligence systems tend to benefit younger employees, but not for the reasons you might expect.

New research published in INFORMS journal Business Administration provides valuable insights to business leaders about the impact of work experience on employees’ interactions with artificial intelligence.

In this study, two main forms of human work experience—narrow experience defined by the amount of specific tasks and broad experience characterized by overall seniority—were used to examine the dynamics within human-AI teams. We are investigating the impact on

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“We developed an AI solution for medical record coding at a publicly traded company and conducted field research with knowledge workers,” says Weiguang Wang of the University of Rochester. “We were surprised by what we found in our research: Different dimensions of work experience clearly interact with AI and play a unique role in human-AI teaming.”

“While some might think that less experienced workers should benefit more from the help of AI, we find the opposite, that AI benefits workers with more task-based experience. At the same time, even though senior employees have more experience, they gain less from AI than junior employees,” said Guodong (Gordon) Gao, Johns Hopkins Carey School of Business. says.

Seniority and AI trust dilemma

Further research revealed that the relatively low productivity gains from AI were not the result of seniority per se, but rather a high sensitivity to imperfections in AI, which led to a decline in trust in AI. .

“This finding presents a dilemma: Experienced employees are well-positioned to leverage AI for productivity, but senior employees who take on greater responsibility and care about their organization They tend to avoid AI because they are aware of the risks of relying on it.” Aid. As a result, they are not using AI effectively,” said study co-author Ritu Agarwal of the Johns Hopkins Carey School of Business.

The researchers urge employers to carefully consider the types and levels of experience of different workers when implementing AI into jobs. New employees with little work experience are at a disadvantage when it comes to utilizing her AI. On the other hand, senior employees with more experience in an organization may be concerned about the potential risks posed by AI. Addressing these unique challenges is key to productive human-AI teaming.

Reference: “Friend or enemy? Artificial Intelligence and Teaming Workers with Different Experiences” Weiguang Wang, Guodong (Gordon) Gao, Ritu Agarwal, October 11, 2023. Business Administration.
DOI: 10.1287/mnsc.2021.00588

Source: scitechdaily.com