Probability of Occurrence

Project Managers use a combination of experience, insight, and quantifiable data to assess potential project risks. In project management, determining the probability of occurrence is one factor in the overall risk assessment and planning work. For the Project Management Institute’s (PMI) Project Management Professional (PMP)® certification exam, and as part of continuous skill development, it is important to understand risk assessment and how it leverages the probability of occurrence.

Risk Assessment and Management

Calculating risk is both an art and a science. Project managers are responsible for identifying risks for projects and managing the work to maximize, prevent, and/or mitigate them. Why would risk be managed to maximize the impact? If it is deemed a favorable risk or in other words, an “opportunity.” Perhaps the risk leads to the outcome of reduced costs or being first to market thus increasing sales. All risks are not bad and some lead to innovations and positive outcomes. For risks with a potential negative impact, referred to as “threats,” the project manager should guide the work to prevent or mitigate the chances of it occurring.

An uncertain event or condition that, if it occurs, has a positive or negative effect on one or more project objectives.
Source lexicon
PMP Formula Cheat Sheet

PMP® Exam Formula Cheat Sheet

Learn how to successfully use project management formulas after reading this cheat sheet.

Assessing a risk is part of what is sometimes referred to as “probability of occurrence pmp.” One of the first steps in a risk assessment is examining each risk and determining if it is an opportunity or a threat. For risk assessment, it must have a risk-neutral assumption for proper judgment between opportunities and threats.

Favorable OutcomeNegative Outcome
 + ValueValue
Risk Type

From here, the project manager needs to do a risk assessment of the probability of that each risk could happen.

Probability Defined

A risk has the potential for a favorable outcome or a negative outcome, and in either case there is an outcome that should be considered during planning. Project Managers, including those working to earn a PMP® credential status, need to know the meaning of probability as part of risk assessment efforts.

Probability Likelihood of an event occurring

Project managers use tools like expert judgement or historical information from past projects to determine the probability of a particular risk occurring. Probability matters for risk assessment and management because if there is a low probability of a risk, resources may need to be directed towards those risks with a high probability of occurrence.

Probability Formula

The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favorable events possible and the total number of events possible.

The Probability of Occurrence is a formula that takes the number of favorable events that can occur and divides that by the total number of events that can occur.

As with all project management tools, the probability of occurrence formula PMP is directly impacted by the accuracy of the data used within it. It is a simple mathematical calculation, but if the risk assessment work is lacking in considering the occurrence of risk, the result is not useful.

Probability Calculation Example

Anyone who has been part of a “let’s just flip a coin” has in fact used the probability of occurrence formula.

Probability of Occurrence Calculation Example

A coin has two sides: one side (“heads”) is Side A, and the other (“tails”) is Side B. The coin is tossed in the air, and the question is, what are the chances, the “probability” if you will, that it will land on Side A. This is that moment when a coin is tossed in the air and witnesses say quickly “Heads!” or “Tails!” reflecting their guess as to which side will land face up. In project management terms:

  • Total number of events = 2 (because the coin can either show Side A or Side B) 
  • Total number of favorable events = 1 
  • The probability of showing Side 1 = (Number of favorable events) / (Total number of events)
  • = 1/2
  • = 50%
  • Probability of showing Side A is 50% 

Probability is one dimension of risk. A risk assessment is incomplete without the other risk dimension: impact.

Impact Assessment Defined

Impact value is the term for the cost to the project if a risk occurs. It is always expressed as a monetary value.

Impact ValueCost of work and resources used to address an identified risk when it occurs
– Source

Probability and Impact Matrix

A risk can impact both costs and schedule. A probability and impact matrix, or as some call it, the probability and impact matrix PMP, connects the probability of a risk and the impact of that risk.

Probability and Impact Matrix
A grid for mapping the probability of occurrence of each risk and its impact on project objectives if that risk occurs.
Source lexicon

With insights around probability and impact, the risk assessment work moves to determining the monetary value of risk for the entire project.

Estimated Monetary Value (EMV)

The risk dimensions, probability of occurrence (uncertainty) and impact (effect) are captured in the Estimated Monetary Value (EMV) formula. EMV is a statistical technique in risk management used to quantify risks and calculate the contingency reserve

Estimated Monetary Value can be calculated with the Probability and Impact values in the Probability of Occurrence formula.

The greatest weakness in the EMV formula is in the accuracy of probability and impact values. The strength of the EMV formula is providing a means to quantitatively prioritize a risk within a set of known risks. With the risk identified, and each assessed by probability of occurrence and the impact value, the estimated monetary value can be determined with these steps:

  1. Assign a probability of occurrence for the risk.
  2. Assign monetary value of the impact of the risk when it occurs.
  3. Multiply the values produced by step 1 and step 2.
  4. Add values to the project cost to calculate total EMV.

There are many tools and modeling techniques for risk assessment. It is important to understand the concepts behind risk assessment so that the right tool or model can be selected, and of course, in support of PMP® certification exam questions around core risk concepts.

Challenges of Risk

The probability of occurrence formula may be easy math, but PMP® credential holders and experienced project managers know there is much more to consider. The PMI® paper “Describing probability: the limitations of natural language” authors provide these insights around common challenges in risk management work for project managers:


  • “…All projects are unique in some respect…This is particularly true of project risks, which affect project objectives. This means that some (many?) risks on a particular project will be unique to that project, and there will be no relevant data on their probability of occurrence.” (excerpt from Describing probability: the limitations of natural language)

Lack of actuals

  • “…Of course some risks on a given project will have arisen previously, since not all aspects of every project are completely unique. However even for these risks, data are often not available from previous projects due to the weakness of the project closure process in many organisations… Without such “risk actuals” from previous projects, the task of assessing the probability of risks which recur on a later project is made more difficult.” (excerpt from Describing probability: the limitations of natural language)

Unknown risks

  • “…Sometimes risks are identified for which some details are inherently unknowable, including for some risks the probability of occurrence. This can arise where occurrence of the risk is dependent on influences outside the project (such as the decisions and actions of other stakeholders or competitors), or where the project team lack the necessary knowledge to understand and assess the risk, or in the case of uncertain events which are in the realm of pure chance.” (excerpt from Describing probability: the limitations of natural language)

Estimating vs. measuring

  • “…further problem with assessing risk probability is that risks are possible future events that have not yet occurred, and as such their probability of occurrence cannot be measured but can only be estimated. However such estimates tend to be influenced by a wide range of subjective and unconscious sources of estimating bias, making them unreliable.” (excerpt from Describing probability: the limitations of natural language)

It is important to know the probability occurrence and impact value for each risk. It is equally important to keep the challenges of risk assessment top of mind to better manage the project work.

Probability and Impact for the PMP® Certification Exam

For the PMP® certification exam, questions may provide students with the probability of a risk occurring and then ask students to calculate the financial impact of risk on a project. Determining the probability of a risk is outside the scope of PMP® certification exam questions.

PMP® Certification Exam Question Example

Unfortunately, risk analysis was not done regularly by the previous manager of a project you inherited. As you are performing the project work, you and your team are reviewing all potential risk events, and analyzing their current probability and impact. Which of the following best describes what you are doing?Critical path method (CPM)Risk re-assessmentSensitivity analysisExpert judgment
You are conducting interviews with key project stakeholders to assess the probability and consequences of identified risks to the project objectives, assign a risk score to each risk, and create a list of prioritized risks. Which process are you performing?Quantitative Risk AnalysisPlan Risk ManagementIdentification of RisksQualitative Risk Analysis

Studying for the PMP Exam?


  1. The answer is B. Risk re-assessment involves reviewing the various risk events to determine whether their probability or impact has changed since your initial assessment (done during planning). This is an important part of Monitor Risks, and should be performed regularly throughout the project.
  2. D. The purpose of Perform Qualitative Risk Analysis is to determine what impact the identified risk events will have on the project and the probability of occurrence. It also puts risks in priority order according to their effects on the project objectives and assigns a risk score for the project. Finally, this process examines the timing of the risk events so those which are upcoming in the near future can be addressed first.


Risk assessment is a challenging task that requires intuition, experience, and qualitative data to provide reliable inputs to the overall risk management process and work. With proper risk management, project managers can assess and prioritize hazards so the “Probability of Occurrence PMP” is low. They can formulate mitigation and contingency plans according to the probability of occurrence pmp and implement them in the most economical way.

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Megan Bell
Megan Bell
Project Manager & Writer at Project Management Academy
Megan Bell