Base Rate Fallacy: Definition & Example

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  • 0:01 Base Rate Fallacy Defined
  • 1:17 Why it Occurs
  • 1:56 Base Rate of a Coin Toss
  • 4:35 Lesson Summary
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Lesson Transcript
Instructor: Alyson Froehlich

Ali teaches college courses in Psychology, a course on how to teach in higher education, and has a doctorate degree in Cognitive Neuroscience.

Why do most people think that if you flip a coin a few times, getting a string of heads is less likely than any other particular combination of heads and tails? In this lesson, you will find out how this and other examples of base rate fallacy occur.

Base Rate Fallacy Defined

Over half of car accidents occur within five miles of home, according to a report by Progressive Insurance in 2002. You may recall having heard this statistic before, or something similar, and being surprised. After all, it takes only minutes of driving to travel five miles from home. How could an accident occur so quickly? However, if you think through this statistic a little further, it's really not so shocking after all. How often do you drive more than five miles from home? If you are like most of us, it's not an everyday occurrence. It's no wonder most of our car accidents occur within five miles of home; that's where most of our driving occurs.

This example illustrates a very common error in judgment. Base rate fallacy occurs when a person misjudges the likelihood of an event because he or she doesn't take into account other relevant base rate information. What do we mean by relevant base rate information? Well, base rate concerns the likelihood of an event occurring out there in the world regardless of what the conditions of a particular situation may be. So, the base rate of being a Christian is 1 in 3 people. The base rate of Americans adults who own cell phones is 9 out of every 10 American adults. We could find the base rate of other things, such as the likelihood of a building having a 13th floor, or the likelihood of a dog being a Labrador.

Why it Occurs

Anytime a certain event occurs, such as a car accident within five miles from home, we can come up with an idea of how likely that event was given relevant base rate information. Relevant base rate information in this case would be things like the likelihood to be within five miles from home when driving, the likelihood of getting into a car accident at all, the likelihood of driving during a particular day of the week or time of day, and so on. However, base rate fallacy occurs because people tend to ignore all of this relevant base rate information and instead rely on mental shortcuts, such as the idea that a car accident occurs when we do a lot of driving, rather than during a quick trip to the local grocery store.

The Base Rate of a Coin Toss

Let's take a look at another example. Suppose I flip a coin 5 times. I then do this a second time. In the first round, I get heads, tails, heads, heads, tails. In the second round, I get tails all five times. Which of these two instances is most likely? Most of us, even those of us who know the correct answer, want to say that the first instance is more likely than the second. I mean, how often does one get five tails in a row? Nevertheless, both instances are equally likely to occur. Each time we flip that coin, there is a 50/50 chance of getting either heads or tails, and what we get on one flip doesn't change the odds for what we will get on the next flip.

Let's look at those odds a little more closely. The chances of getting tails on any given flip of a coin is 50%, or 1 out of 2. The chances of getting tails on the next flip would be our current odds (1 out of 2) multiplied by the odds of getting tails on any flip (1 out of 2). That makes the odds of getting 2 tails in a row 1 out of 4. Do this a few more times, and we end up with odds of 1 out of 32 for getting a string of 5 tails in a row.

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