Planning With Probabilities

Probability and statistics can manipulate your thinking. We know that, and yet we don’t always use it to our advantage.

It isn’t that hard.

How probability works

Suppose there is some improbable event. Maybe the odds are one in a thousand of it happening. Can we ignore it?

We can, but it might not be smart to do so. Probability of occurrence shows us only part of the picture. If I know the odds of something are 1000 to one against, I must further notice those are the odds for one particular occurence.

What if there a thousand people exposed to the possibility. The question of how many must there be so the odds are 50-50 that any person in the group is affected? Now we don’t know. We have made the probability a two-factor question.

The N-p Problem

Outcomes depend on p — the probability, and N — how many instances are there where the probability has applied. In our thousand person group with 1 in a 1000 probability, there is no way to discover when the odds are even. Instead you calculate the number of times it theoretically won’t happen. For example, if there are four people involved, the odds of it not happening are .999 to the power four = .996. Four chances in 1000 it happens. So the odds are about 250 to 1 against. With 20 people .98 = .02 chance probability = 1 in 50.

How many for 50-50? One in two chances. At 694 instances the probability of no occurrence is .4994, so about 1 in 2 times it happens. Probability when there is a 1000 people in the group will not be zero, it is after all a probability not a certainty. With 1000 people the probability of no occurrence is 36.7%. Even with 3000 people there is a 5% chance nothing has happened. With 5,000 just 0.6% chance of no event. Even if you ran it 1,000,000 times, 45 times it would not happen.

If you care about the occurrence happening somewhere or sometime, the probability does not matter and the Number of instances does. In physics there is a law that says unless something is specifically prohibited, it will eventually happen. For a large enough N you can believe in certainty.

Low probability and won’t happen

People frequently mistake low probability to mean “won’t happen.”  That is not quite true.

What are the odds of a small community college football team beating the defending NFL champion Tampa Bay Buccaneers? Probably ten million to one against. That is true if they play just one game. But what if they play seven million games? What are the odds they have won at least once? (1 -.9999999^7000000) = about 50-50.

Life is like that too.

Applying N-p to life

You might not be able to control p, but you often can control N. Suppose you want to meet someone who could become your significant other. You assess the odds of going to a coffee bar and succeeding as one in a hundred. You can increase the probability of a successful outcome by increasing N, even if you accept p as one in a hundred. You might want to think what would make p better too, but that’s a harder question.

If you went to a coffee bar twice a week for a year, it would turn out the odds that you will meet someone are nearly two to one in favour. You don’t know who or when or where though. In the common vernacular, “It’s a numbers game.”

There are other factors that matter. One of them is you cannot go to the same bar on the same day of the week, at the same time, because the crowd may be the same every time.  Probability works when the trials are independent.

The meeting does not fully define the outcome. Meeting a prospective person is not enough. There is a follow up need too. It matters more.

Hindsight tells us something.

When we look at history we can see why some things happened. The observation seems inevitable even. It’s because we see only the outcome. We don’t see the other N-1 times nothing happened.

When looking ahead you cannot focus only on the event. It might be a failure. People who achieve highly improbable things do so by not being affected by the “didn’t happen today” outcome. Thomas Edison built at least a thousand lightbulbs before he found one that worked. You could estimate the odds of success using that information, but it would not be easy. You will be stuck with the fact he found it on the 1000th try. Would the odds have been necessarily different if the found it on the 5th try. Maybe, but you cannot be sure.

Life isn’t certain.

As long as it is not, you should do two things.

  1. Find ways to make probability even slightly better in your favour.
  2. Increase N

If you are in sales that means improve your presentation and see more people.

If you are looking for a significant other, improve your presentation and see more people.

The takeaway

Probability affects you every day. Its effects are not inscrutable so pay some attention.

Learn a little , and do more, it will improve the number of successful outcomes

Notice that you cannot easily see the things that didn’t happen, even though you know they must have.

Never forget you care most about outcomes not probabilities. That’s why N matters.


I help people have more retirement income and larger, more liquid estates.

Call in Canada 705-927-4770, or email don@moneyfyi.com

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: