A solid understanding of statistics is crucially important in helping us better understand finance. In probability theory and statistics, Bayes' theorem alternatively Bayes's theorem, Bayes's law or Bayes's rule describes the probability of an event, based on prior knowledge of conditions that might be related to the event. However, we know the probability of event A under condition B and the probability of event A under condition C.

The total probability rule states that by using the two conditional probabilities, we can find the probability of event A. The total probability rule also called the Law of Total Probability breaks up probability calculations into distinct parts.

The Law of Total Probability is one of the most important theorems in basic Probability theory. What is the probability that the ball is red?

This is the idea behind the law of total probability where each cost of the pen is replaced by the probability of an event A. One bag is selected at random and a ball is selected at random from that bag. Events B and C are distinct from each other while event A intersects with both events. The return on the investment is an unknown variable that has different values associated with different probabilities.

## Total Probability Theorem

Learn more about different types of probabilities, or explore hundreds of other calculators covering the topics of math, finance, fitness, and health, among others. We basically do the partitions in the sample space S, to calculate the single probabilities and add then at the end.

All of these m ways will have some value for the probability. Note how closely it resembles 1our original LoTP. What percent of students passed the test? The total probability gives us an idea of the likelihood that an event is supposed to occur or not. Your email address will not be published. Home Uncategorized law of total probability calculator. Uncategorized September 23, 0 Comments 0 A solid understanding of statistics is crucially important in helping us better understand finance.

If you like this post, please share to others. Leave a Comment.If A and B are two independent events in a probability experiment, then the probability that both events occur simultaneously is:.

In case of dependent eventsthe probability that both events occur simultaneously is:. You have a cowboy hat, a top hat, and an Indonesian hat called a songkok. You also have four shirts: white, black, green, and pink.

If you choose one hat and one shirt at random, what is the probability that you choose the songkok and the black shirt?

### Bayes Rule Calculator

The two events are independent events; the choice of hat has no effect on the choice of shirt. There are three different hats, so the probability of choosing the songkok is 1 3. There are four different shirts, so the probability of choosing the black shirt is 1 4. Suppose you take out two cards from a standard pack of cards one after another, without replacing the first card.

What is probability that the first card is the ace of spades, and the second card is a heart? There is only one ace of spades in a deck of 52 cards. If the ace of spaces is drawn first, then there are 51 cards left in the deck, of which 13 are hearts:. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. Varsity Tutors connects learners with experts.

Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials. Example 2: Suppose you take out two cards from a standard pack of cards one after another, without replacing the first card. Subjects Near Me. Download our free learning tools apps and test prep books. Varsity Tutors does not have affiliation with universities mentioned on its website.Bayes' theorem is a mathematical equation used in probability and statistics to calculate conditional probability.

In other words, it is used to calculate the probability of an event based on its association with another event. The theorem is also known as Bayes' law or Bayes' rule. It would be more accurate to refer to the theorem as the Bayes-Price rule, as Price's contribution was significant. The modern formulation of the equation was devised by French mathematician Pierre-Simon Laplace inwho was unaware of Bayes' work.

Laplace is recognized as the mathematician responsible for the development of Bayesian probability. There are several different ways to write the formula for Bayes' theorem. The most common form is:. P A and P B are the probabilities of A and B occurring independently of one another the marginal probability. You might wish to find a person's probability of having rheumatoid arthritis if they have hay fever.

In this example, "having hay fever" is the test for rheumatoid arthritis the event. Plugging these values into the theorem:. So, if a patient has hay fever, their chance of having rheumatoid arthritis is 14 percent.

It's unlikely a random patient with hay fever has rheumatoid arthritis. Bayes' theorem elegantly demonstrates the effect of false positives and false negatives in medical tests.

A perfect test would be percent sensitive and specific. In reality, tests have a minimum error called the Bayes error rate. For example, consider a drug test that is 99 percent sensitive and 99 percent specific. If half a percent 0. Only about 33 percent of the time would a random person with a positive test actually be a drug user.

The conclusion is that even if a person tests positive for a drug, it is more likely they do not use the drug than that they do. In other words, the number of false positives is greater than the number of true positives. Share Flipboard Email. Anne Marie Helmenstine, Ph. Chemistry Expert. Helmenstine holds a Ph. She has taught science courses at the high school, college, and graduate levels.

Facebook Facebook Twitter Twitter. Updated August 12, Use the calculator below to find the area P shown in the normal distribution, as well as the confidence intervals for a range of confidence levels. Probability is the measure of the likelihood of an event occurring. It is quantified as a number between 0 and 1, with 1 signifying certainty, and 0 signifying that the event cannot occur.

It follows that the higher the probability of an event, the more certain it is that the event will occur. In its most general case, probability can be defined numerically as the number of desired outcomes divided by the total number of outcomes. This is further affected by whether the events being studied are independent, mutually exclusive, or conditional, among other things. Given a probability Adenoted by P Ait is simple to calculate the complement, or the probability that the event described by P A does not occur, P A'.

Any P B' would be calculated in the same manner, and it is worth noting that in the calculator above, can be independent; i. Consider the probability of rolling a 4 and 6 on a single roll of a die; it is not possible. These events would therefore be considered mutually exclusive.

In this case, the probabilities of event A and B are multiplied. To find the probability that two separate rolls of a die result in 6 each time:. The calculator provided considers the case where the probabilities are independent. Calculating the probability is slightly more involved when the events are dependent, and involves an understanding of conditional probability, or the probability of event A given that event B has occurred, P A B.

Take the example of a bag of 10 marbles, 7 of which are black, and 3 of which are blue. Calculate the probability of drawing a black marble if a blue marble has been withdrawn without replacement the blue marble is removed from the bag, reducing the total number of marbles in the bag :.

As can be seen, the probability that a black marble is drawn is affected by any previous event where a black or blue marble was drawn without replacement. Thus, if a person wanted to determine the probability of withdrawing a blue and then black marble from the bag:. In probability, the union of events, P A U Bessentially involves the condition where any or all of the events being considered occur, shown in the Venn diagram below.

In this case, the "inclusive OR" is being used. This means that while at least one of the conditions within the union must hold true, all conditions can be simultaneously true. There are two cases for the union of events; the events are either mutually exclusive, or the events are not mutually exclusive. In the case where the events are mutually exclusive, the calculation of the probability is simpler:.

A basic example of mutually exclusive events would be the rolling of a dice where event A is the probability that an even number is rolled, and event B is the probability that an odd number is rolled. The calculator above computes the other case, where the events A and B are not mutually exclusive.The probability of an event is the chance that the event will occur in a given situation.

The probability of getting "tails" on a single toss of a coin, for example, is 50 percent, although in statistics such a probability value would normally be written in decimal format as 0. The individual probability values of multiple events can be combined to determine the probability of a specific sequence of events occurring.

To do so, however, you must know if the events are independent or not. Tip: This same approach can be used to find the probability of more than two events. Michael Judge has been writing for over a decade and has been published in "The Globe and Mail" Canada's national newspaper and the U.

Michael has worked for an aerospace firm where he was in charge of rocket propellant formulation and is now a college instructor. First, watch the video below for a quick refresher on basic probability:. Determine the individual probability P of each event that is to be combined.

Determine if the two individual events are independent or not. Independent events are not influenced by each other. The probability of heads on a coin toss, for instance, is not affected by the results of a prior toss of the same coin and so is independent.

Determine if the events are independent. If not, adjust the probability of the second event to reflect the conditions specified for the first event. For example, if there are three buttons -- one green, one yellow, one red -- you may wish to find the probability of picking the red and then the green button. Multiply the individual probabilities of the two events together to obtain the combined probability.

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Learn more Calculating the probability of multiple events is a matter of breaking the problem down into separate probabilities and the multiplying the separate likelihoods by one another.

Note: The probability of the 5s being rolled are called independent events, because what you roll the first time does not affect what happens the second time. Probability is the likelihood that a specific event will occur. To calculate probability, first define the number of possible outcomes that can occur. Now define the number of events. In this example, the number of events is 2 since 2 days out of the week fall on the weekend. Finally, divide the number of events by the number of outcomes to get the probability. No account yet? Create an account. We use cookies to make wikiHow great. By using our site, you agree to our cookie policy. Learn why people trust wikiHow. Explore this Article methods. Probability Cheat Sheets. Tips and Warnings. Related Articles. Article Summary. Method 1 of All rights reserved. This image may not be used by other entities without the express written consent of wikiHow, Inc. Choose an event with mutually exclusive outcomes. The event and its opposite both cannot occur at the same time.

Rolling a 5 on a die, a certain horse winning a race, are examples of mutually exclusive events. Define all possible events and outcomes that can occur. Here are 2 more examples to help you get oriented:  X Research source Example 1 : What is the likelihood of choosing a day that falls on the weekend when randomly picking a day of the week?

Example 2 : A jar contains 4 blue marbles, 5 red marbles and 11 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is red?This is easy to do with a tool called the Strategic Risk Severity Matrix. Whatever the reason, the Strategic Risk Severity Matrix is a fantastic tool to help you make a data-driven determination. On the bottom are the Probability factors, which is how we rate the likelihood that the event will happen.

We can use this tool to calculate whether negative outcomes will happenand if so how destructive the effects could be.

calculate and interpret an unconditional probability using the total probability rule;

Our scoring is done when we select a level of Impact 1 to 5and a level of probability 1 to 5. A score is determined by the product multiplication of the two numbers. This number is associated with a 5-level scoring result Controlled, Serious, Disruptive, Severe, or Critical. Controlled a score of 1 to 2 — Limited monitoring only Serious a score of 3 to 6 — Active monitoring Disruptive a score of 8 to 9 — Investigation needed Severe a score of 10 to 16 — Rapid action is required Critical a score of 20 to 25 — Immediate, crucial priority.

Upon reviewing your numbers, it is clear that several customers have decided to stop using your services. You want to know whether this is a significant problem or one that can just be monitored. Rather than pointing blame or trying to solve the problem right away, a better approach is to state the problem logically.

Next, we want to set a numeric equivalent for the amount of impact — the degree of negative change that will or could happen due to this problem. Another consideration is what effect this shift is having on other customerson staff, or on projected sales targets. In our example, 3 of the 12 departing customers are highly profitable. This loss could affect future sales, especially if those were repeat customers and loyal buyers. Note: I always suggest that you conduct a Post-Mortem Evaluation for any change in customers to find out what went wrong and why.

You can also find some gems of wisdom by having an Offboarding process, where departing customers can express their complaints or reasons for leaving — this is an invaluable source of information that can be applied to decision-making.

### Total Probability Rule Calculator

A financial analysis at this point to determine the profit margins could reveal whether this problem will continue to affect sales. If you know for certain that this change will not cause tremendous long-term problems, then you could comfortably pick the 3rd level of Impact:. Without further data, we need to assume that this risk is fairly high.

So our finding for this particular situation is that it has a very high probability Frequent and moderate impact Serious. A score of 15 puts this in the Severe range a score between 10 and 16which means rapid action is required. We also know the same thing could continue to happen unless we conduct a Root Cause Analysis aka Post-Mortem Review and investigate the reasons for customers who already departed.

As you can see, this risk management tool is a really easy way to visualize the impact of risk. You can use it to evaluate current problems, potential future problems, or as part of a Post-Mortem to evaluate what happened in the past and how to correct it. If you feel frustrated with running your company and want to discuss ways to adjust your strategy, find out more here. Grace LaConte is a business consultant, writer, workplace equity strategist, and the founder of LaConte Consulting.

Her risk management tools are used around the globe, and she has successfully reversed toxic work environments for clients in the healthcare and non-profit fields. Find more at laconteconsulting. This site uses Akismet to reduce spam. Learn how your comment data is processed. Skip to content. Why Does Severity Matter?

On the left side, we see Impact factors, or severity if the event occurs.