# Subjective Probability: Definition & Examples

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## What is Subjective Probability?

With subjective probability, you use knowledge and opinions, not calculations.

## What is Subjective Probability?

Subjective probability is where you use your opinion to find probabilities. For example:

• You think you have an 80% chance of your best friend calling today, because her car broke down yesterday and she’ll probably need a ride.
• You think you have a 50/50 chance of getting the job you applied for, because the other applicant is also very qualified.
• You’re taking your dog to the vet today, and based on past experience you’re pretty confident you’ll need over \$100 for the bill.

No calculations are involved in subjective probability; it involves opinions (usually based on your past experiences) only.

## The Downsides

As only personal opinions are involved, there is usually a high degree of personal bias. Another downside is that one person’s opinion may differ vastly from another’s. For example, you might think the Jacksonville Jaguars are going to find themselves at the bottom of the league this year, while your friend (a Jags fan) may argue that they have some great new players and certainly won’t.

A third problem that affects subjective probability is that they must obey certain conditions in order to be workable. For example, you can’t think there’s a 75% chance of rain today and also think that there is a 75% chance of it not raining; probabilities must add up to 100%. As you aren’t performing calculations, it’s easy to fall into the trap of failing to meet this condition for more complicated probabilities.

## What is it Used For?

If subjective probability is so open to bias, why use it at all? We often think of probability in terms of the classical probability definition, which is the number of favorable events, divided by the total number of events. However, this is one narrow case of probability and it isn’t suitable for all areas of the field, including Bayesian probability. A more philosophical approach is to realize that probabilities only have meaning to the person thinking about them (i.e. you). Being subjective when calculating probabilities is a way of quantifying the unknown and is a necessary part of life.

Let’s say that you’ve been to your dentist twice, and have spent \$125 and \$150 each time. You hear through the grapevine that the dentist has upgraded his office and that his fees have “skyrocketed.” You have two choices:

1. Guesstimate (i.e. use subjective probability) that you budget \$300 to cover the potential bill.
2. Go to the dentist with no idea what the cost is going to be, receive a bill for \$375, and completely destroy your budget.

Obviously, you’d want to go with the guesstimate!

## Subjective Probability Examples in Real Life

In real life, we have to act, choose, decide, guess, and judge on imperfect information [1]. It’s this imperfect information that leads us to use subjective probability to make decisions. As it’s basically an educated guess based on your personal judgement, anything you can make a probability statement about could fall under the guise of subjective probability. For example, all of the following are subjective probability examples in real life situations:

• I think that the president has a 25% chance of being elected again.
• You think that a recession is about to hit, and you want to calculate the impact to your business. You have no data to look at, because your business hasn’t been through a recession. But based on what the last recession did to your friend’s business, you think it’s 90% likely you’ll see a significant drop in income.
• A friend applies for a job with three other candidates. As they all seem equally qualified, you think there’s a 25% chance your friend will get the job.
• You buy a new metal detector and go hunting on the beach. As this is in an area known for artifacts, you think there’s a 90% chance of finding an interesting or valuable object.
• Despite the fact that John drinks, eats unhealthy food, and doesn’t exercise, he thinks he has a 99% chance of living until 100.
• You think there’s a 90% chance someone will land on Mars in the next ten years.
• Due to your late night study group, you think you have a 99% chance of passing tomorrow’s math test.

Subjective probability is also the basis for many logical fallacies, old wives’ tales, and rules of thumb. This is especially true in gambling, which is governed by the rules of probability that are obscured by gamblers’ superstitions and intuition about “luck” [2].

## References

[1] Cohen, J. & Hansel, M. Risk and Gambling: a study of subjective probability. Retrieved October 25, 2021 from: https://prism.ucalgary.ca/bitstream/handle/1880/526/age.pdf?sequence=1&isAllowed=y
[2] Freund, J. (2012). Introduction to Probability. Courier Corporation.

Haase, N. The Measurement of Subjective Probability. Retrieved April 8, 2016 from here.

CITE THIS AS:
Stephanie Glen. "Subjective Probability: Definition & Examples" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/subjective-probability/
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