Class 5

What Are the Chances? Probability as the Language of Uncertainty

Formalising the uncertain judgements that every workplace risk assessment already depends on

You Already Think in Probabilities

Every time you assess a psychosocial hazard, you are making a probabilistic judgement. When a consultant writes that a team faces a "high risk" of burnout due to excessive workload, they are asserting - whether they realise it or not - that the probability of burnout is elevated given a particular workplace condition. When a regulator flags job insecurity as an "emerging concern," they are claiming that the base rate of harm from this hazard is rising across the workforce (Schulte et al., 2024).

The problem is not that we lack probabilistic intuitions. The problem is that our intuitions are unreliable. Decades of research have demonstrated that people systematically neglect base rates, overweight vivid or recent information, and struggle to combine multiple pieces of evidence coherently (Tversky & Kahneman, 1974; Ortoleva, 2024). In workplace contexts, this means a manager who recently witnessed a bullying complaint will overestimate the prevalence of bullying across the organisation, while underestimating quieter hazards like role ambiguity. Kopp (2025) has shown that these biases are not fixed - they shift depending on whether the judgement context feels abstract or concrete - which means they can be shaped by the tools we use.

Probability gives us those tools. Let us begin with the simplest idea.

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Marginal Probability: The Baseline

Marginal probability is the likelihood of an event occurring without considering any other information. Think of it as the base rate. If organisational survey data show that 30% of workers in the healthcare sector report high psychological distress, then the marginal probability of high distress for a randomly selected healthcare worker is 0.30.

Why does this matter? Because base rates are the starting point for all further reasoning. If you are assessing a particular hospital team and you ignore the sector-wide base rate, you have no anchor - no way to judge whether the team's situation is better or worse than expected. Tversky and Kahneman (1974) famously demonstrated that people routinely neglect base rates when given vivid case-specific information, a finding that has been replicated in workplace risk assessment contexts (Kopp, 2025). The first discipline of probabilistic thinking is to always ask: What is the baseline?

In the language of Karasek's (1979) demand-control model, we might express several base rates simultaneously. In a given industry, perhaps 40% of roles involve high demands, 25% involve low decision latitude, and 15% involve both - the high-strain combination. These marginal probabilities set the stage for a much more powerful question.

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Conditional Probability: Context Changes Everything

Conditional probability answers a different question: what is the likelihood of an event given that we already know something else? It is written as P(A | B), read as "the probability of A given B." This small notation captures an enormous conceptual leap.

Consider the difference between these two questions:

• Marginal: What is the probability that a worker in this organisation experiences psychological distress?
• Conditional: What is the probability that a worker experiences psychological distress given that they have both high demands and low control?

The second question is far more useful. Research using the demand-control model consistently shows that the conditional probability of distress given high-strain conditions is substantially higher than the marginal probability of distress across the whole workforce (Karasek, 1979; Morin et al., 2020). Morin and colleagues found that workers in "iso-strain" profiles - high demands, low control, and low social support - represented the highest-risk configuration, a finding that only becomes visible when you condition on multiple hazards simultaneously.

Conditional probability is also the mechanism behind the workplace observation that hazards rarely act alone. The probability of turnover given low pay might be modest. The probability of turnover given low pay and poor management and limited career progression is something else entirely. Each conditioning piece of information reshapes the probability landscape. This is precisely the kind of complex interaction that deterministic checklists cannot capture but that probabilistic models handle naturally.

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Bayes' Theorem: Reasoning in Reverse

Marginal and conditional probabilities let us describe the world. Bayes' theorem lets us learn from it. It is the mathematical rule for updating beliefs when new evidence arrives, and it addresses the "direction problem" we identified in Chapter 3: traditional risk assessment reasons forward - from hazards to harm - but what if we need to reason backward, from observed harm to its likely causes?

Here is the intuition. Suppose you observe that a team has high absenteeism. Multiple hazards could explain this. Bayes' theorem tells you how to start with your initial beliefs about each possible cause (your prior probabilities), consider how well each cause explains the evidence you have observed (the likelihood), and arrive at revised beliefs (your posterior probabilities).

Posterior belief ∝ Prior belief × Likelihood of the evidence given that belief

In more precise terms: P(Hazard | Evidence) = P(Evidence | Hazard) × P(Hazard) / P(Evidence). But the formula matters less than the logic. Bayes' theorem says: your new belief should be your old belief, adjusted by how strongly the evidence supports it relative to all other explanations.

Consider a concrete scenario. You initially believe there is a 40% chance that a team's distress is driven by excessive workload, a 35% chance it is driven by poor change management, and a 25% chance it is driven by interpersonal conflict. Then you learn that exit interviews consistently mention "unclear roles and responsibilities." This evidence is much more likely under poor change management than under the other two hypotheses. Bayes' theorem will therefore increase your posterior probability for change management and decrease the others - even though you have not directly measured change management at all.

This is backward reasoning: moving from an observed effect (exit interview themes) to an updated belief about an upstream cause (change management failure). It is precisely what Bayesian networks, the subject of our next chapters, will automate across dozens of interconnected variables.

Why Natural Frequencies Help

If the formula feels daunting, there is good news. Gigerenzer and Hoffrage (1995) demonstrated that Bayesian reasoning becomes dramatically easier when we think in natural frequencies rather than abstract percentages. Instead of saying "the probability of high distress given high strain is 0.60," imagine 100 workers: 15 are in high-strain roles, and of those 15, about 9 report high distress. This concrete framing - "9 out of 15" - activates the same Bayesian logic but feels intuitive rather than mathematical. Rosenberg et al. (2022) have shown that frequency-based activities significantly improve students' ability to update beliefs correctly and even shift their broader understanding of how knowledge is constructed under uncertainty.

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Try It: The Belief Updater

The interactive widget below puts Bayes' theorem into practice with a realistic workplace scenario. Set your prior beliefs, predict how evidence should change them, and then compare your intuitions against the mathematically correct update. Research suggests your intuitions will improve with practice (Rosenberg et al., 2022) - so cycle through all three evidence scenarios.

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Why Probabilistic Reasoning Beats Checklists

The traditional approach to psychosocial risk assessment relies on deterministic checklists: Is this hazard present? Yes or No. But as Schulte et al. (2024) document, psychosocial hazards are not binary switches - they exist on continua, they interact with each other, and their effects depend on context. A checklist that asks "Is workload excessive?" cannot distinguish between a team at 60% probability of burnout and one at 90%. Probability can.

More critically, checklists only reason forward. They can tell you which hazards are present, but they cannot tell you which hazards most likely explain the patterns of harm you are already observing. Bayes' theorem enables this backward reasoning - what Ortoleva (2024) describes as the fundamental advantage of Bayesian updating over simpler heuristic strategies. When a Bayesian network encodes the relationships among dozens of psychosocial variables, Bayes' theorem propagates evidence in both directions simultaneously, updating every node in light of whatever you observe. The checklist asks you to fill in boxes. The Bayesian network asks you to share what you know and then tells you what it implies.

This is not to say that human judgement is worthless. On the contrary - your prior beliefs, your contextual knowledge, your professional experience - these are essential inputs to the Bayesian framework. The framework does not replace judgement; it disciplines it, making your reasoning transparent, consistent, and open to revision as new evidence accumulates.