Our Random World—Probability Defined

From the lecture series: What Are The Chances? Probability Made Clear

By Michael Starbird, Ph.D., The University of Texas at Austin

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.

Game and probability theory concept
(Image: ImageFlow/Shutterstock)

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?

This is a transcript from the video series What Are The Chances? Probability Made Clear. Watch it now, on The Great Courses Plus.

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.

Learn more about the concept of randomness and its quantification through probability 

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.

probability of rain
Probability gives us information that we can act on (Image: alfaori/Shutterstock)

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.

Learn more about a numerical way to make decisions 

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.

Pediatrician injecting vaccine
In the medical field, making decisions based on probability can be quite difficult. (Image: Olena Yakobchuk/Shutterstock)

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.

Learn more about probability can be used to model the distribution of genetic traits 

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.

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.

Gaussian, bell or normal distribution curve and histogram
Here the normal probability distribution allows us to draw meaningful conclusions about the random outcomes plotted on the histogram . (Image: marekuliasz/Shutterstock)

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 glimpses of regularity. It’s the job of probability to put a meaningful numerical value on the things that we admit we don’t know.

Common Questions About Probability

Q: What exactly is probability?

Probability is a mathematical possibility of what might occur when one takes part in a mathematical potential such as rolling dice or choosing an item off a menu.

Q: Are there two or more types of probability?

There are many types of probability: experimental, theoretical and subjective probabilities are the most commonly understood.

Q: What is an example of probability?

A coin toss is the most common example of probability. With a 50 percent chance of either heads or tails, we see both sides of the issue.

Q: Is simple probability different from probability?

Simple probability is simply the probability of an outcome such as a roll of the dice or choosing an item from a menu.

This article was updated on 8/23/2019

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