Our Random World—Probability Defined

FROM A LECTURE SERIES TAUGHT BY Professor Michael Starbird, Ph.D

While it’s nice to think that our challenge in life is to get rid of uncertainty and be in complete control of everything, that is not going to happen. One of life’s real challenges is to deal with the uncertain and the unknown in some sort of an effective way; and that is the realm of probability.

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What Are the Chances? Probability Made Clear
Explore the fundamental concepts and fascinating applications of probability in this fun and engaging course by an award-winning mathematician.

 

The Chances We Take…

Let’s say you buy a lottery ticket; what are the chances that you’re going to be rich for the rest of your life?

You walk across a golf course in a stormy day; what are the chances you’ll be hit by lightning?

What are the chances that your investments will allow you to live happily for the rest of your days?

You have a fever; you have a cough. What are the chances that it’s a serious disease rather than something trivial?

All these are real-life examples of situations where we’re confronted with possibilities whose outcomes we do not know. In fact, I would argue that many or most parts of our lives—and the world and trying to understand the world—involve situations where we don’t know what’s going to happen. They involve the uncertain and the unknown.

Probability Defined

It would be nice to say, “Well, our challenge in life is to get rid of uncertainty and be in complete control of everything.” That is not going to happen. One of life’s real challenges is to deal with the uncertain and the unknown in some sort of an effective way; and that is the realm of probability.

umbrella for probability article
Probability gives us information that we can act on.

Probability accomplishes the really amazing feat of giving a meaningful numerical description of things that we admit we do not know, of the uncertain and the unknown. It gives us information that we actually can act on.

For example, when we hear there’s an 80% chance of rain, what do we do? We take an umbrella. Of course, if  it doesn’t rain, we say, “Well, there was a 20% chance it wouldn’t rain. That’s okay.” If it rains, we say, “Oh, yes, the prediction was right. There was an 80% chance of rain.”

Probability is a rather subtle kind of a concept because it can come out one way or the other, and still a probabilistic prediction can be viewed as correct—but decisions made on probability have all sorts of ramifications.

When we make medical decisions, for example, we are making decisions that are based on probabilities, and yet they have extremely serious consequences, including life and death consequences.

In the case of the rain, all we risk is getting wet. But in many areas of making decisions on the basis of probability, there are very serious consequences. When we make medical decisions, for example, we are making decisions that are based on probabilities, and yet they have extremely serious consequences, including life and death consequences.

An Ethical Quandary

Back before probability was viewed as commonplace as it is today—  between 1750 and 1770 in Paris, there was a smallpox epidemic for which a vaccine was developed. Unfortunately, the inoculations were rather risky. They reckoned that there was a 1 in 200 chance of death from taking the inoculation, but on the other hand, there was a 1 in 7 chance of dying eventually from the disease. So making that kind of decision is a very dramatic question where we’re weighing probabilities.

closeup image of child receiving vaccine
In the medical field, making decisions based on probability can be quite difficult.

If you took that inoculation and you died immediately from smallpox, did you make the right decision or not? Well, of course, you don’t want to be among the 1 in 200 that died from the inoculation. On the other hand, on the basis of probability, it was the right decision. There are many controversies about this kind of thing and in today’s world with lawsuits and all this would be a very serious kind of an issue to undertake.

Well, in many arenas of life, our understanding of the world comes down to understanding processes and outcomes that are probabilistic in nature, that really come about from random chance, that things are happening by randomness alone. Over the last couple of centuries, the scientific descriptions of our world increasingly have included probabilistic components in them.

Probability In Higher Studies

Many aspects of physics all involve questions of probability. Things we imagine—molecules causing things to happen by the aggregate force of probabilistic occurrences—quantum mechanics — thermodynamics. At the very foundations of our knowledge of these studies is the theory of probability.

Biology, genetics, and evolution are all based very centrally on random behavior, as well. In fact, in all of these areas, the goal is to make definite, predictable, measurable statements about what’s going to happen that are the result of describing random behavior.

Image of double helix strand for probability article
At the very foundations of our knowledge is the theory of probability.

The description of random behavior is how we, as scientists and mathematicians, define the world. This is a major paradigm shift in the way science has worked for the last 150 years. As time goes on, there continues to be an increase in the role of probability and randomness at the center of scientific descriptions.

Probability gives us a specific statement about what to expect when things happen at random. But how can it be effective when, by definition, random outcomes of one trial or one experiment are completely unknown? Well, if you repeat those trials many, many times and look at them in the aggregate, that’s when you begin to see glimses of regularity. It’s the job of probability to put a meaningful numerical value on the things that we admit we don’t know.

From the lecture series What Are The Chances? Probability Made Clear
Taught by Professor Michael Starbird, Ph.D.

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