Probability Calculator

The Probability calculator allows you to calculate the probability of an event occurring by entering the number of events and the total number of outcomes. The key to a successful single event probability calculation and multiple event probability calculation is to correctly define the total number of outcomes. We explore the importance of correctly calculating the total outcomes later, first, lets get familiar with the probability calculator.

Probability Calculator
Probability Calculator Results and Calculations
Single Event Probability (P(A)) that the event will occur
Probability that the event will occur %
Single Event Probability that the event will not occur
Probability that the event will not occur %
Single Event Probability Calculation
P(A) = n(A)/n
Probability that the event will occur Calculation
Single Event Probability that the event will not occur Calculation
Probability that the event will not occur Calculation
Probability Calculator Input Values
Number of events (e) %
Number of possible outcomes (o)

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 Probability Calculator: This image shows Probability formula and algorythms associated calculations used by the Probability Calculator

About the Probability Calculator

The probability calculator has two inputs:

  1. Number of Events: The number of events in probability is the number of opportunities or success. So, for example, there are ten runners in a race, 2 of the runners are wearing blue. If we wanted to calculate the probability of the winner of the race being a runner wearing blue, we would enter 2.
  2. Number of outcomes: The number of outcomes in probability is the number or mutually exclusive outcomes. This means if one event occurs, the other event cannot. So, in our runners in a race outcome, any one of the ten runners can win the race. When one of the runners wins the race, the remaining 9 runners lose the race. So there are 10 mutually exclusive outcomes as any of the ten runners can win whilst, at the same time, making the other 9 losers. In each winning scenario, the individuals in the losing group are different so winner and losing group are mutually exclusive.

In the probability calculator, we use the following letters which are later used within the probability formula to allow you to understand how probability properties are calculated and how the probability calculator calculates probability.

  1. e = Number of events (that can occur)
  2. o = Number of possible outcomes

Probability Explained

Probability is perhaps the single most used math term and something we calculate, not necessarily to precision, but as part of our lives everyday. We use the probability of an event occurring to make informed decisions as to whether we complete an action. For example, if there is a high probability that it is going to be a very hot and sunny day, we would use that knowledge to apply sunscreen. This example highlights how probability is used most, to access the likelihood of an event (or multiple events) occurring to calculate the risk. Probability plays a significant role in Health and Safety Risk assessments for this very reason.

What is Probability?

Probability is basically another word for chance, chance being a word that we use more often in everyday conversations than probability. Probability Chance) is the measurement of how likely it is that something (an event, or multiple events) will happen. So, out entire lives are made up of probability as we assume life itself is a series of accidents and/or random events, therefore, there are endless possibilities of what could occur, each of these single or multiple events or outcomes can, be defining the properties, be measured as a probability.

What is the unit of measurement for probability?

Probability is most commonly shown as fractions though it can be displayed as decimals. Probability measurement as a decimal is more practical when you intend to use the calculated probability as part of an additional formula, for examples to complete a risk assessment as mentioned earlier. Probability can also be measured as a percentage or said as a statement, typically when referring to chance, for example a 1 in 5 chance of occurring.

Probability measurement units

As we discussed previously, there are several measurement units for probability, here are examples of measurement units for a race with six horses which, for the sake of this argument, are exactly equal.

  1. 1 in 6: Probability expressed as a verbal expression, typically associated with chance (online gambling, regular gambling and betting etc.)
  2. 0.1666: Probability expressed as a decimal number, typically when necessary for use in further mathematical calculations
  3. 1/6: Probability expressed as a fraction, very useful for quickly identifying the quantity of options and the number of calculated chances of occurrence
  4. 16.666%: Probability expressed as a percentage is particularly useful in making risk assessment, both physical and financial. For example, there is an 80% probability of seeing a 5% return on your investment.

As with all numbers which can be expressed as a fraction, Probability can also be expressed as a ratio.

Single Event Probability and Multiple Event Probability?

We have mentioned single event probability and multi event probability a few times, lets look at each in more detail. A single event probability can be defined as the probability of an outcome when something occurs just once. For example, the probability that a coin will land heads up when spun on a flat surface, let's try a math experiment.

Single Event probability

Lets start with a simple example that illustrates single event probability calculations.

An example of a Single event probability is the spinning of a coin.

  1. Take any coin
  2. Place it between your finger and thumb
  3. With your hand close to a flat surface (a table for example), apply rotational force to the coin using your finger and thumb causing the coin to spin.
  4. The coin will spin for a period of time, gradually slowing.
  5. When the coin eventually stops spinning, it will fall either heads up or tails up.

The probability that the coin will land either heads up or tails up is 1 in 2, 0., 50% or ½.

This was a single event probability exercise; you spun the coin once. Well, that is unless you failed to spin the coin, there is probability involved there too. In this example, we have of course gone with the standard example of a coin which provides a useful lesson in probability. The key to defining a good probability calculation is understanding and defining all possible outcomes. So, when we spin the coin, there are 2 outcomes right - Heads up or tails up? Wrong there are three possible outcomes. There is also the probability that the coin will stay on its side. This probability depends on the aspect of the coin (rounded edge coin or a flat coin), it is however still a probability though less likely than the probability of heads up or tails up. Defining the true probability would involve knowing the full properties of the coin, is it evenly balanced weight wise, is in machine perfect of are there imperfections in its shape? How wide are the edges of the coin, are the coin edges flat or textured? As with all great math and sciences discoveries and insights, full understanding comes with looking at the detail. This is truly why the coin example in math probability is an excellent lesson, it perfectly illustrates how easy it is to make assumptions in math tests / math exercises and by doing so, arrive and the wrong result using the right math formula. The devil is in the detail.

Single Event Probability Formula

In a single event probability calculation we look to calculate the probability of the event occurring, that is being true, AND we can also calculate the probability of the event not occurring, that is being false. In this way, probability is on its basic level a binary calculation.

Probability Formula: Probability of event occurring

The following formula can be used to calculate if an event will occur and therefor be true.

P = e/o


  • P = Probability
  • e = Number of events (that can occur)
  • o = Number of possible outcomes
Probability Formula: Probability of event not occurring

The following formula can be used to calculate if an event will not occur and therefor be false.

P = 1 - e/o


  • P = Probability
  • e = Number of events (that can occur)
  • o = Number of possible outcomes

Multiple event Probability

Multiple event probability is very similar to a single event probability, simply repeated several times. So, if we were to repeat our spinning coin example, the probability of it landing heads up changes with each repetition. In fact, there are some interesting properties of probability defined with multiple probability formula. For example, you can measure what may occur, what may not occur and then the resultant probability given the outcome of the previous result.

Why do need to know the probability of an event occurring

In maths, it is probably the most often ask question and something math teachers come to expect from their math students, "why do I need to know how to calculate this in math?", "why is such and such useful in math?", "how will this math formula help me in my life?". The great news for math teachers when teaching probability, is that it is essential. Whether crossing the road, making financial decisions, making business decisions or making decisions about starting a family, the comprehension of probability is essential. Of course, not any of us will sit down and assess the full risk of starting a family by working out all the probability involved but the comprehension of probability allows us to correctly calculate risk (whether ate a defined mathematical level or on a perception level). Probability is both a practical skill and perceptual skill and although technically, the practical calculated probability is the true defined math probability, we should not underestimate the computing power of the human brain, even if it does not produced a defined number, well, at least not one we can yet quantify. In time, probability measurement of the human brain via binary on / off will be quantifiable. Who knows, you may well one day be using iCalculators probability calculator via a neural-control interface.

How is probability used in real life

As we have discussed, probability is everywhere in life though perhaps most commonly identified with gambling. Gambling, sports gambling being a good example, is littered with events which can, to a greater or lesser degree, be quantified to the point when probability calculations and accurate enough to allow bookkeepers to provide betting odds on the successful outcome of one or more results. For example, a single bet on a dog winning a race or multi bets on several different horses wining different races, or coming second, third etc. In modern, times, you can even bet on who will be the first to score a goal in a football match. All of these betting odds are computed by calculating probability.

I safety, probability is used to makes key decisions. For example, all roads present a danger to pedestrians. The probability of harm however differs depending on speed, visability, surface, number of previous accidents and so forth. Identifying the probability of an accident occurring allows government highways bodies to reduce the risk of accidents in areas identified as high risk due to the calculation of probability of accidents.

Probability summary

Well, if you made it this far, we hope you enjoyed our look at probability as mush as we did. Probability is such an interesting topic as it covers so many aspects of life and is a key part of how we thing on a scientific and spiritual level about our lives. It is key in the discussion of life by design or accident. The fact that we can document and measure probability illustrates that life is a series of random events. It also suggests that we are each, mathematically, capable of influencing and changes those events. We are each capable of calculating probability to either make something happen or make it not happen. We believe, probability is perhaps the most amazing part of the world of maths.

And finally, Don't Panic!!!

We could hardly discuss the subject of probability with mentioning the genius that was Douglas Adams. His inspired wit and deep insight provided some truly excellent and hilarious moments for millions around the world. If you have read his work, there is a high probability that there is hole in your life where his wonderful insights should be. So, in a word of endless probabilities, we give you the infinite improbability drive:

Infinite Improbability Drive

The Infinite Improbability Drive is a wonderful new method of crossing vast interstellar distances in a mere nothing of a second without all that tedious mucking about in hyperspace.

It was discovered by a lucky chance, and then developed into a governable form of propulsion by the Galactic Government's research team on Damogran.

This, briefly, is the story of its discovery.

The principle of generating small amounts of finite improbability by simply hooking the logic circuits of a Bambleweeny 57 sub-meson Brain to an atomic vector plotter suspended in a strong Brownian Motion producer (say a nice hot cup of tea) were of course well understood - and such generators were often used to break the ice at parties by making all the molecules in the hostess's undergarments leap simultaneously one foot to the left, in accordance with the Theory of Indeterminacy.

Many respectable physicists said that they weren't going to stand for this - partly because it was a debasement of science, but mostly because they didn't get invited to those sort of parties.

Another thing they couldn't stand was the perpetual failure they encountered in trying to construct a machine which could generate the infinite improbability field needed to flip a spaceship across the mind-paralysing distances between the furthest stars, and in the end they grumpily announced that such a machine was virtually impossible.

Then, one day, a student who had been left to sweep up the lab after a particularly unsuccessful party found himself reasoning this way:

If, he thought to himself, such a machine is a virtual impossibility, then it must logically be a finite improbability. So all I have to do in order to make one, is to work out exactly how improbable it is, feed that figure into the finite improbability generator, give it a fresh cup of really hot tea ... and turn it on!

He did this, and was rather startled to discover that he had managed to create the long sought after golden Infinite Improbability generator out of thin air.

It startled him even more when just after he was awarded the Galactic Institute's Prize for Extreme Cleverness he got lynched by a rampaging mob of respectable physicists who had finally realized that the one thing they really couldn't stand was a smartass.

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