# expressing probability qualitatively

My mother in law gave me a pack of playing cards for Christmas, and I immediately noticed the flag of Puerto Rico on the back.  (She lives there now for part of the year conducting disaster relief missions on a retired Navy ship.  Buying a pack of “local” playing cards as a souvenir on family trips—or every time we move—is kind of an informal tradition in our family.) I opened the pack today, and only found forty-eight cards.  I was confused.  Apparently it’s a pack of Spanish playing cards, and if you search Naipes Comas on the internet, you’ll see what I did when I started looking through the deck.  That’s just an aside though—I put them back and grabbed a more familiar set of cards.

I want to use playing cards to conduct a thought experiment, so go to the game closet or your desk and grab a deck, or you can simply imagine you did.  Shuffle the deck and deal yourself a normal hand of five cards.  This is the hand I dealt.

It may require you to brush the rust off a part of your brain that you vaguely remember, but I want us to answer an important question: how likely is this hand of cards?

This is the kind of thing listed in FAA Order 4040.26C, Appendix C, paragraph 3.e., “Perform a risk assessment by: (1) Estimating the probability of each hazard occurring.”

Frequent
Probable
Occasional
Remote
Improbable

Have you decided?

## Communicating Quantitatively and Qualitatively

“Engineering is done with numbers. Analysis without numbers is only an opinion” (David Akin).

In the previous issue of the FTSF, I made an offhand comment, that I was disappointed that we were still expressing probability qualitatively in our risk assessments.  Several members of the committee wrote an op ed describing their arguments in support of this position (above).

Akin sums up my feelings succinctly with his quote above, but I want to use the thought experiment above to more fully explore ways to communicate about uncertainty and make recommendations that include both qualitative and quantitative means of communicating.

How likely is this hand of cards?

I don’t know what your answer is to the question first posed above, but I think we can agree that not everyone had the same qualitative answer.  Probability gives us the tools to formally compute this quantitatively.

I said “quantitatively” not perfectly.

For example, is there more than a 50% chance this thing will happen? Is there less than a 50% chance this thing will happen?

This is “quantitatively”!

I once did a test program to investigate the effects of a leaky brake valve, a manufacturing defect that was discovered on in service aircraft.  We had already done several taxi tests, so I understood the behavior of the valve.  The engineering team modified the aircraft to demonstrate the worst case scenario, total failure on one valve.  Only one toe brake worked.

I was almost certain that we would depart the prepared surface during testing, which included a build-up of simulated “aborts” from slow speed to high speed.

There are two things I want to point out:

1. Sometimes “avoid” is not the right answer.

We needed to know what would happen to a pilot who experienced this during landing or an aborted takeoff roll.  The risk of not knowing outweighed the safety risk, the combination of probability and hazard.  Knowing would help us develop procedures to address the failure.

1. I could put a number on my beliefs.

In the description above, I used “almost certain,” but there is another thing I am almost certain about: we all have different meanings for the phrase.