# The Probability of Chance

I have just returned from a trip to Singapore where I was facilitating a workshop to set up the initial risk register and risk management plan for a \$1 billion project to deliver one package in a multi billion oil development. The beginning of November is also the Spring Racing Carnival in my home state featuring the Melbourne Cup – the race that literally stops the nation. The combination of these two events and many hours sitting in aeroplanes started me thinking about the difference between project risk and the more widely understood actuarial risks managed by insurance companies and the like.

I have already posted on some of the challenges faced by project risk managers dealing with a single occurrence, the project, using theories based on constrained probability distributions in large populations (see: A Long Tail); and written a number of papers on risk management, see: http://www.mosaicprojects.com.au/Resources_Papers.html#Risk. This post looks at the challenges from a different perspective, how people in project teams perceive and understand probability.

The Singapore workshop started with the consideration of range statements for two sets of parameters, the likely impact of a risk event and the probability of it occurring. The outcomes were quite straightforward:

• >\$20 million was seen as a very high impact risk through to <\$500,000 for a very low impact risk.
• >70% probability was seen as a very high probability through to <5% for a very low probability.

The valuation of a ‘very high impact’ was based on a percentage of the project’s anticipated profit. Interestingly, the project manager for the overall project (some \$20 billion investment) thought the monetary values were on the high side but accepted the views of the engineering company I was working with.

The focus of this post is on the difficulty of assessing probability based on limited data for a one off event such as a project. The following simple scenario illustrates the problem:

There are 3 sealed envelopes – one contains \$100.

As a starting point, most people would agree there is a 33.33% chance any one of the envelopes will contain the money.

If we open one envelope and it is empty, there is now a 50:50 chance either of the remaining envelops has the money. One does, one does not.

Now to make the situation interesting…….

I give you one envelope and keep two for myself.

As a starting point you have a 33.33% chance of having the money and I have a 66.66% chance – the odds in my favour are 2 envelopes to your 1 envelope

Now I open one of my envelopes and we see it is empty. What does this do to the probabilities?

One perspective says there is now a 50:50 chance the money is in your envelope and 50:50 it is in my envelop – we know it has to be in one or the other and it has not moved.

On the other hand nothing has changed the original starting scenario – the odds in my favour were 2:1 and at least one of my envelopes had to be empty so on this basis is there still twice the probability my remaining envelop has the money compared to yours…… we have done nothing to improve your chances, you still only have one out of the three original envelopes!

Which scenario best represents the situation and why??

Now to make the situation even more interesting….

If I was to offer you \$40 for your envelop would taking the money be a good or a bad bet???

If the scenario suggesting a 50:50 chance is true, the Expected Monetary Value (EMV) of your envelope is \$100 x 50% = \$50

If nothing has changed the starting scenario the EMV of the envelope is \$100 x 33.33% = \$33.33.

Which option is correct????

Peter de Jager posed a similar question to the PMI Melbourne chapter and favours the 2:1 option remaining true, many of the chapter disagreed.

Any thoughts would be appreciated.

### One response to “The Probability of Chance”

1. Thanks for your reflections on project and actuarial risk and its unifying thread of probability. You might be interested in http://www.dynamicalsoftware.com/news/?p=61 which relates project risk with financial risk.