Thursday, December 08, 2022

A Deep Dive into Probability Distribution in Risk Management

Ever tossed a fair coin? I’d bet you have! At least in your childhood days while deciding which team would bat first in a baseball or a cricket match, or who would serve first in a badminton or tennis game. Every kid agrees to it because it’s unbiased. When you toss a fair coin, the chances of getting a head is 1/2 (0.5) or 50%. This is the division between the favorable outcome, which is a head and all possible outcomes (head and tail).

A coin toss is perhaps is the simplest introduction to probability, which informs chance or likelihood of occurrence of a random variable. The random variable here is getting a head. Let’s note the random variable as X and probability as P(X). Mathematically put:

Probability (Getting head) or P (X)

= Favorable number of outcomes of the event / Total number of possible outcomes

= 1 / 2 = 0.5 = 50%

Now, what’s the chance of getting a head when you toss a pair of coins together? In this case, the total number of possible outcomes is four: tail (first coin) and tail (second coin), tail and head, head and tail, and finally head and head. The values that the random variable can take are many, as shown in the below table:

As you can see, the possible values of X range from 0 to 2 (i.e., 0 head, 1 head, or 2 heads). This leads to the concept of distribution. Looking at the above table, we can see the frequencies of this random variable’s occurrences are 1, 2, and 1. This is distribution or frequency distribution. One could say: distribution is the possible values a random variable can take and how frequently these values occur.

Now, if I add probabilities to this random variable’s values, we get a probability distribution. This is depicted in below:

As shown in the above table:

  • We have all favorable outcomes for 0, 1, or 2 heads. These are represented in the first and second columns.
  • All possible outcomes are obviously four, and that’s shown in the third column.
  • P(X) is shown in the final column, and the probabilities are 25%, 50%, and 25%, respectively for 0, 1, or 2 heads. This is probability distribution. Summed up, it equals one.

Hence, we can say that probability distribution for a random variable describes how probabilities are distributed over the values of the random variable.

Discrete and Continuous Distribution

Distribution can be discrete or continuous. Discrete means you are getting an integer number (1 head or 2 heads). You don’t say that you will get 0.33 head! Considering another example of counting the number of children in households of a locality, you will come-up with results such as 0 child, 1 child, 2 children, etc. You won’t get 0.57 child!

You may be laughing now – what’s 0.33 head or 0.57 child!? Good to see you smiling. Smiling lessens stress and helps in understanding.

All random variables; however, are not discrete. For example, let’s say you are determining the distribution of age, weight, or height of people in a locality. Considering height, it can be anything: 5 feet, 5.5 feet, 5.85 feet, 6.1 feet, and so on. In such a case, the distribution is continuous. So, this distinction is important: at a high-level, there are two types of random variables – discrete and continuous and respective probability distributions – discrete probability distribution and continuous probability distribution.

Now, combining all, i.e., probability, distribution and probability distribution, I've the following consolidated tip.

But, how does all of this fit into Risk Management? Risk Managers don’t toss coins or calculate heads/tails in an experiment. That’s kids’ games and not for grown-up men or women! Perhaps; although, child play teaches the basics neatly.

Probability Distribution and Risk Management

With the above basics, let’s consider another example to understand probability distribution from the perspective of risk management. You are going to a friend’s house. It may take you one hour to reach your destination if you encounter no obstacles. If there is heavy traffic, it’s possible that you may not get there for three hours. With less traffic, it’s more likely to take 2 hours. Hence, you can say there are three possibilities:

  • Minimum (or Optimistic) travel duration = 1 hour
  • Most likely travel duration = 2 hours
  • Maximum (or Pessimistic) travel duration = 3 hours

In this case, the random variable (X) is the “travel duration.” Can you conclusively say which one of the estimates is correct? Unlikely, because other factors such as traffic conditions are involved. Now, if I add chances to these numbers, then we get probability distributions. I’ve prepared the below video to explain in more detail [Duration: 05m:33s]. For better audio-visual experience, you may want to go full HD and plug-in your earphones.

Importance of Probability Distribution *** UPDATED ***

In project risk management, the concept of probability distribution is applied to estimation. Continuing with our previous example, when we estimate, we take the most likely outcome of two hours, which is not correct because we’ve forgotten to consider other possibilities.

We can (and should!) consider possible scenarios, not just the most likely one. In other words, instead of saying an activity in a project is going to take “X” number of days, we also can consider other days using a distribution. For each duration in the distribution, there is a probability available.

This can be done for all the activities or tasks of the project, which in turn impacts the project schedule and cost. This enables us to build a more realistic plan.

Now that we have understood the basics of probability, distribution, and probability distribution, let’s look at the various types used in risk management.

Triangular Distribution *** UPDATED ***

Triangular distribution is the most common type of distribution used.  Named triangular because of the shape of the curve, this refers to there being no pre-existing data, but only expert opinions or judgment.

Symmetrical Triangular Distribution

The below distribution is triangular and symmetrical.


By looking at the graph above, we can say: There is approximately a 30% chance of the duration being 6 days, a full chance of the duration being 8 days’, and also a 30% chance of the duration being 10 days.”

Asymmetrical Triangular Distribution

Do note that the triangle shown need not be symmetric. Asymmetrical diagrams are shown below:

From here, you can calculate the durations with respective chances or probabilities.

Let’s take another example of a project, once with a task of Product Requirement Documentation (PRD) Preparation with an estimated 5 days duration. This is the most likely estimate, but we do not have the minimum and maximum value.

By using the Primavera Risk Analysis (PRA) software tool, the triangular distribution is depicted as below:


The durations can be 4, 5, or 6 days (shown in the X-axis). The respective chance for minimum, likely, and maximum values are entered when you perform a duration risk analysis. This is demonstrated in a video in the later part of this article.

While building the schedule model, this triangular distribution can be noted as Triangle (4, 5, 6) or Triangle (4; 5; 6).

Uniform Distribution

In rectangular distribution, you can use a maximum value and a minimum value, but not any most likely value. In the below example, we have a uniform (or rectangular) distribution.

Looking at it, we might say: The task has a minimum duration of 4 days, but a maximum duration of 12 days

You can use Uniform Probability Distributions when you specify the extremes of uncertainty of the activity under consideration and when the intermediate values have equal chances of occurring. It is also possible when you cannot draw any inference on the possible distribution shape.

Taking our previous example of the PRD Preparation task, which is estimated to be 5 days, using PRA, we have the following values for Uniform distribution:

Like Triangular distribution, while building the schedule model, this distribution can be noted as Uniform (4, 6).

Beta Distribution *** UPDATED ***

Beta distribution, like triangular distribution has also three possible values – worst case, most likely, and best case. Like the triangular model, it also gives more weightage to the most likely case. We have seen one example of Beta distribution in the earlier video.

Unlike the triangular distribution, the shape for beta distribution is smoother and the tails in Beta distribution taper off less quickly. A sample beta distribution curve is shown below:

Beta distribution can also be symmetric or asymmetric in shape. The notations happen like Beta (6, 8, 10). As you can see above, there can be many values close to the most likely values, and it slowly tapers off towards the minimum or maximum ends.

Using the PRA software tool, for our task, PRD Preparation, a Beta (or BetaPert) distribution will come out as below:

Do note that along with the triangular distribution, beta distribution is another frequently used probability distribution.

Normal Distribution

Normal distribution is defined by the mean of a planned (or remaining duration) activity for an activity and standard deviation (SD) of the activity.

This distribution is used if there is historical information available. Normal distribution also has a bell-shaped curve like Beta, but considers SD to calculate the worst (and best) case scenarios. 

For our example (task of PRD Preparation with a duration estimate of 5 days), we note the normal distribution as Normal (5,1), where 5 is the mean and 1 is the SD.

Discrete Distribution

In a discrete distribution model, the duration of an activity under consideration can have a number of integer values, but without any intermediate values. In other words, the distribution is discrete, rather than continuous like in a triangle, beta, or uniform.

In the above sample, the activity has discrete distribution of values 6, 10, 18, and 20. 

Considering our task of PRD Preparation, the discrete distribution will be seen as below with the PRA tool. The distributions are 2, 3, 4, and, 5 with respective weighting factors of 10, 20, 30 and, 50, respectively. This can be noted as Discrete ({2, 3, 4, 5}, {10, 20, 30, 50}).

Practical Example and Demonstration

With this understanding, let’s take a practical look using MS Project and Primavera Risk Analysis. The video [Duration: 05m:42s] demonstrates a project plan with fixed activity estimates. It’s next imported to the PRA tool and analyzed with various probability distributions for the activities of the project.


Probability distribution is very important when you use quantitative risk analysis, which involves a number of mathematical modeling and sampling. Managers or planners can also deploy advanced probability distributions such as lognormal distributions, cumulative distributions, general distributions, among others. The above video explains a few of these.

We have come a long way and seen a number of examples. I propose just one more exercise. I promise it won’t be difficult, provided you have read the content sincerely. Going back to our first examples of coin tosses, can you answer these:

  • What’s the probability distribution of getting a head when you toss three coins?
  • What are the values that the random variable can take?

If you are getting four values for the random variable of getting a head and when all your probability distributions are summed-up to equal one, then you have well understood the concept. 

I welcome your thoughts, feedback, and suggestions in the comment section below.

* This article is dedicated to the memory of my father, the late Harendra Nath Dash, who passed away three years ago on June 11, 2019. He first introduced me to the concept of probability and statistics. It was mesmerizing then, and I still remember it. I wish this article to be a tribute to him and his teachings.


This article was first published by on 7th June, 2022. The current one is updated.

Sunday, November 27, 2022

Step-by-Step Guide: Install, Set-up and Run MS Project 2019/2021 with Agile Features (Online Desktop Client)

Summary: MS Project has full in-built Agile features available for the Online Desktop Client version. When customers purchase my courses of Mastering MS Project Agile and/or Certified Hybrid-Agile Master Professional (CHAMP) courses, the first question that comes up is: how to see these features in MS Project? 

In fact, many struggle to install and hence can't use the Agile and Hybrid-Agile features. In this post, you will learn how to install, set-up and run MS Project in a step-by-step manner.

Note: Though I've mentioned MS Project 2019/2021 software with Agile Features, it’ll work with the latest version of MS Project. I personally use the software. The software is released continuously and when you download, you will get the latest version. You have to just follow the below steps.

Frequently Asked Questions (FAQs)

First and foremost, I receive the below questions frequently from the customers, users and aspiring users who want to buy the courses. Hence, I’ll address them first.

Question – 1: I already have a licensed version of MS Project installed. It does NOT have Agile features. What should I do?

Answer – 1: Simply uninstall the existing software. Go ahead and install MS Project 2019 Online Desktop client. You can try for one month and more. 

If you want to revert back to your earlier version, then simply uninstall the current Online Desktop Client and install your earlier version. It’ll work as you have the licensed version.

Question – 2: I do NOT have any version of MS Project software installed. But I want to use the Agile features. What should I do?

Answer – 2: Follow the steps mentioned in this post. After the MS Project Online Desktop Client is installed, you can run and check the Agile features.

Question – 3: How do I know that the MS Project Online Desktop Client has installed properly with its Agile features?

Answer – 3: Follow the steps mentioned in this post. I’ve shown a clear demonstration on how to install, run and check the Agile features. In the final step, I've informed on the verification with respect to Online Desktop Client.

Question – 4: Will I get a PDF version for installation steps when I go for the courses of Mastering MS Project Agile and/or Certified Hybrid-Agile Master Professional (CHAMP)?

Answer – 4: Yes, absolutely. You will have detailed step-by-step instructions with complete explanation, when you subscribe to the either or both of the above courses. You will also have detailed video explanations on how to check the Scrum, Kanban, ScrumBan, Hybrid-Scrum, Hybrid-Kanban, Hybrid-ScrumBan with these courses. 


MS Project Agile/Hybrid-Agile Installation, Set-up and Run

MS Project Agile features for installed software in your computer is only available in the Online Desktop Client edition. It’s not available in any other version of the software. The MS Project for the Web, a new version of MS Project, is fully online or web-based. But it’s completely different. Hence, we will start with downloading the MS Project Online Desktop version and proceed with the below steps.

Step – 1: Know where the software is available

The software is available at the below link: 

As you can see there are three plans:

  • Project Plan 1:
    • Available for free one-month trial and then nominal payment.
    • This plan does NOT have Online Desktop Client.
  • Project Plan 3: [Use this plan]
    • Available for free one-month trial and then a bit more nominal payment
    • This version has an Online Desktop Client as shown in the column (check the next figure). 
  • Project Plan 5:
    • This plan also has an Online Desktop Client. 

You can learn more on these plans at the below link:

Specifically, in our case, we will take Project Plan 3. This has the least cost and maximum number of features available. Also, unlike Plan 5, for Plan 3 we don’t have to contact any partners.

As you can see the Desktop Client and its features can be used on upto 5 PCs.

Step – 2: Create an account at

The office portal the one where you have all the office related software available for download, such as MS Word, MS PowerPoint, MS Excel etc. If you don’t have an account here, you can create an account at

I assume you already have licensed version of the software available. That way, you can export easily to MS Excel or MS PowerPoint from MS Project software. Yes, MS Project software has a number of features, which you can work with or export to other office software.

After you have created an account at the Office Portal and logged-in, you will have following view. 

As shown, when you login:

  • On your left side, you will have the software available such as MS Word, MS Excel, among others.
  • On your right, you can install all the software as apps.

When you have a subscription for MS Project Plan 3 software, you can use the “Install apps” command on the right and install the MS Project software. This is another way to install the software.

Step – 3: Go to

As informed earlier, we are going to use Project Plan 3, which has the Online Desktop Client. Hence, in the link, we will use that plan.

The below view will be available for you.

In the above view, use the “Try free for one month” option (highlighted above). Later-on, you can pay to continue with the software. 

Step – 4: Provide the needed details to use Project Plan 3 

When you try free option in the previous step, it'll lead you to another page with the below view. 


There are a few steps involved such as providing your email id, verification and minimal business information. Once you are done you are subscribed to Project Plan 3!

Step – 5: Ensure to have the latest release at: 

It’s a good idea to have the latest release available for your software. The software gets updated frequently and with the latest release, you will have the latest features available. 

In the above link (, you will have the following view. 

In the above view, go to Settings > Org settings, which are highlighted. Here, we can have the latest software release setting.

In the Org Settings, select Release preferences under the Name column, as shown below. 

As you click on Release preferences, you will have the following view.


Ensure that the checkbox of "Targeted release for everyone" is selected. 

Now, you are fully ready to download the software and install.

Step – 6: Go to

As you click on the above link, we will find the following view. 

It’s possible that you may get the Download option instead of an Install option. In such a case, don't worry at all. It’s perfectly fine. Just download the software. Ensure that it’s compatible with your OS.

You can go for a 32-bit or 64-bit version of this software. 

Note: If you have purchased an office edition in 32-bit, then use the 32-bit version for Project Online Desktop client. 

Step – 7: Install the Project (Plan 3) software

Do remember that you are now effectively installing a subscription version of the software, with the Online Desktop Client feature as we have seen earlier.

In other words, you downloaded the client side of the software on your desktop via online. This will look exactly like Desktop editions with a slight twist, which we will see in the final step. 

As you install the software and continue, it’ll look as shown below, post installation. 

Step – 8: Check Agile (Scrum and Kanban) Functionality

Now that the software is installed on your desktop, you can run it. 

As shown, the software is now available on Windows Start command. It’s highlighted as Project. As you run the software, the following view comes-up. 

As shown, now you have, capability to run:

  • A Traditional Project,
  • A Sprints (Scrum) Project,
  • A Waterfall project, and also
  • A Kanban Project (it can used from the Waterfall project mode)
In-depth, hands-on videos are available on how to check on such projects with Mastering MS Project Agile and/or Certified Hybrid-Agile Master Professional (CHAMP) courses.

When you click on the Sprints Project command above, you will have the following view. 

Step – 9: Check the Account Information

Finally, you can check that the installed version is Microsoft Project Online Desktop Client.  

This can be seen by going to File > Account > and checking the Product Information as shown above. This is the twist I had mentioned in step - 7 earlier. If you want to have the latest updates, have it enabled to get the latest updates for this software.

Downloadable PDF Copy 

The step-by-step guide is embedded in this post as shown below. It's detailed one and has additional instructions to set-up Project Plan 3 with Online Desktop Client (Agile) features. You can scroll to see the entire content.

As noted before, a downloadable copy of MS Project 2019/2021 online desktop software installation is available to the users of the new Agile courses.

To get more updates on MS Project software related courses and get the complete step-by-step instructions separarately, subscribe to this site (on top right corner of this site) and send a mail, from your Gmail id to 


The detailed step-by-step document is also available in GDrive. 

To access the document in PDF format with detailed instructions, use this link.


[1] NEW Online Course: Mastering MS Project 2019 Agile (Scrum, Kanban and ScrumBan), by Satya Narayan Dash

[2] NEW Certification Course: Certified Hybrid-Agile Master Professional with MS Project, by Satya Narayan Dash

Wednesday, November 23, 2022

Unknowable-unknowns Vs. Unknown-unknowns in Risk Management with Emergent Risks and Novel Risks

As I frequently interact with project and risk management practitioners, the below two questions on unknowable-unknowns and unknown-unknowns come up. They are quite confusing for many. The existing literature doesn’t help as they are written with complicated language and/or complex explanations. The questions are:

  • What are the differences between Unknowable-unknowns and Unknown-unknowns? 
  • Where does emergent risk actually fit in (in the above context)?

To understand, let’s simplify. 

The Fundamentals

First, let’s understand, what is the difference between unknowable and unknown?

  • Unknown: You really don’t know. It’s definitive. 
  • Unknowable: You are not likely (or unlikely) to know. It’s probabilistic. 

When we say definitive, it’s certain that you don’t know. For example, it’s possible you don’t know some new technologies, design or frameworks.

When we say probabilistic, a chance factor comes in. There is a chance (usually high) that you don’t know. For example, when disruptive technologies start to pervade, you are unlikely to know the impact. 

Simply put:

  • When we say unknown, it means there is a lack of knowledge or untapped knowledge.
  • When we say unknowable, it means there is not only lack of knowledge, but also exploration is not probable. In this case, it’s untappable knowledge. 

Now, let’s see what are emergent risks and novel risks? 

Emergent Risks

As per PMI’s Standard for Risks in Portfolios, Programs and Projects, this is the definition of emergent risks:

“A risk that arises which could not have been identified earlier on.”

I agree with this definition, but not the subsequent explanation of PMI on emergent risks in the context of the unknowable, though I’ve adopted them in my books and courses. In this case, one can say these risks could not be identified because they were unknown at that time, but later on, the risks emerged.

When one says “emerge”, a pattern is forming, but not clear. It’ll emerge. 

Novel Risks

I provide this definition for novel risks:

“A risk that arises which was not probable (improbable) to be identified earlier on.”

Here you can say, these risks were improbable to be determined and later it came-up unexpectedly, hence the term “novel” or completely new – not emerging! 

When one says “novel”, there is no pattern formation at all. It is completely new. 

Also, did you notice the distinction in the definitions?

For an emergent risk, we could not have identified earlier, which can be due to many factors such as lack of knowledge, understanding or considering various scenarios. 

For a novel risk, we have a probability factor coming into play. It was improbable to be identified earlier because exploration of such a risk was improbable. 

Unknown-unknowns Vs. Unknowable-unknowns

Now, let’s see the difference between these two:

  • Unknown-unknowns: You don’t know that you don’t know. This is pure ignorance. Knowledge wise, it’s untapped knowledge. It’s part of the Complex domain.
  • Unknowable-unknowns: You are unlikely to know that you don’t know. This is not pure ignorance. Knowledge wise, it’s untappable knowledge. It’s part of the Chaos domain.

The emergent risks are actually unknown-unknown risks or simply unknown risks, whereas novel risks are actually unknowable-unknown risks or simply unknowable risks. Again, do note that my explanation differs from many, including PMI. The figurative representation is shown below.

I’d also strongly recommend that, you read the followings articles:

Cynefin Framework, Risks and Agile: Known-unknowns, Unknown-unknowns, and Unknowable-unknowns

Risk Classification: Known-knowns, Known-unknowns, Unknown-unknowns, and Unknown-unknowns


Combining all that I've explained:

  • Known-known is conscious knowledge or facts. You know that you know.
  • Known-unknown is conscious ignorance. You know that you don't know.
  • Unknown-unknown means unconscious ignorance. You don't know that you don't know.
  • Unknowable-unknown means unexplorable and unconscious ignorance. You are unlikely know that you don't know.

If you have understood so far in this article, then you have understood the difference between unknowable-unknowns, unknown-unknowns and the associated risks such as emergent risks and novel risks. 


[1] RMP Live Lessons - Guaranteed Pass or Your Money Back, by Satya Narayan Dash

[2] RMP 30 Contact Hours, with Full Money Back Guarantee, by Satya Narayan Dash

[3] Book - I Want To Be A RMP: The Plain and Simple Way To Be A RMP, Second Edition, by Satya Narayan Dash 

[4] The Standard for Risk Management in Portfolios, Programs and Projects, by Project Management Institute