Kevin has edited encyclopedias, taught history, and has an MA in Islamic law/finance. He has since founded his own financial advice firm, Newton Analytical.
Using Bayes' Theorem allows you to revise probability values when making decisions. This lesson explains what Bayes' Theorem is and how it is applied in decision making.
More Accurate Predictions
In business, being able to predict the future is no small part of succeeding. No, I'm not suggesting that you resort to crystal balls or tarot cards. In fact, those would probably prove to do more harm than good! However, being able to make the most accurate predictions possible based off of a set of facts is a key skill. That is one of the reasons that Bayes' Theorem is so useful. Unlike simple probability, which only tests the probability of unrelated events, Bayes' theorem allows us to run probability tests on dependent events. This allows us to more accurately base predictions on required events which themselves are not guaranteed. In this lesson, we're going to learn how to use Bayes' theorem, including a walk through of the math involved, before trying it all out in a real-world example.
Before we move on, I want to be sure that you really get just how amazing of a thing this is for business. Before Bayes, it was impossible to really get a handle on how related events would interact. Since so much in business follows on established events, being able to calculate the probability of events makes business predictions so much more accurate.
Not only does Bayes' Theorem allow us to check for future events but also control for false positives. While not as much of a concern in the business world, the scientific and healthcare uses of Bayes' theorem allows for people to calculate the chance that someone identified as a positive match by a test could indeed be a false positive. As you might expect, this information is itself very useful in diagnoses of patients.
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Back to business. Now let's make sure you know how to use the math involved in the Bayes' theorem. From the first, it's a pretty intimidating formula: the probability of A happening if B happens is equal to the probability of A happening times the chance of B happening if A is true divided by the probability of just B happening. Even saying it is a mouthful! However, let's think it through. First of all, let's start with the easy side of the equation. By saying 'probability of A happening if B happens,' I mean exactly that - the chance of A happening after B has already occurred. That's what we're trying to solve. Meanwhile, the hardest part of the rest of that is the 'chance of B happening if A is true' - isn't that the opposite of what we're trying to solve? Well, not exactly. In fact, we're seeing if there is even a chance of A and B coexisting. If the two couldn't coexist, then the whole thing goes to zero! Also, notice that because you're dividing by the probability of B, that has to exist in a form other than zero or else the math simply falls apart.
Let's plug some numbers in to get an idea of how it works. Let's say you were calculating the chance of someone getting chosen for a job interview after getting selected for a summer internship. You know that the chance of being selected for the job interview is 0.1, while the chance of getting selected for a summer internship is 0.4. Meanwhile, the likelihood of those getting job interviews having been summer interns is 0.7. Now let's crunch some numbers. First, multiply the probability of the job interview by the likelihood of those getting job interviews having first been summer interns. 0.1 times 0.7 gives us 0.07. Now, divide that number by the probability of getting a summer internship, or 0.4. That gives us a final probability of getting chosen for a job interview after having been selected for an internship at 0.175.
In this lesson, we learned how to use Bayes' Theorem to be able to predict the outcome of dependent events. Remember that Bayes' theorem is that the probability of A happening if B happens is equal to the probability of A happening times the chance of B happening if A is true, divided by the probability of just B happening. Also, be sure to bear in mind that the probabilities cannot equal zero. If the probability of A and B coexisting is zero, then the probability of A happening if B happens is zero, while if the probability of B happening alone is zero, you are then dividing by zero.
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