Probability Calculator

With the probability calculator, you can find out how likely two different events are in relation to each other. For example, if event A has a 50% chance and event B also has a 50% chance, you can find the probability of both happening, only one event happening, at least one happening, or not happening at all.

Our tool shows you six possible outcomes, plus six additional outcomes if you specify “how many times the die is rolled.” As long as you know the probabilities of individual events, this calculator saves you from lengthy calculations.

By reading further, you can:

Learn how to use a probability calculator effectively;

Understand how to calculate the probability of individual outcomes;

Explore many real-world examples of probability, including conditional probability rules;

See the difference between theoretical probability and experimental probability; and

Strengthen your understanding of how probability relates to statistics.

Probability of Two Events

Probability measures how likely an event is to occur. It ranges between 0 and 1, where 1 means certainty and 0 means impossibility. The closer the probability is to 1, the more likely the event is to occur. In general, probability is the number of favorable outcomes divided by the total number of possible outcomes. The nature of the events – whether they are independent, mutually exclusive, or conditional – affects this calculation.

This calculator helps you determine the probability that event A or B does not occur, the probability that A and/or B occur when they are not mutually exclusive, the probability that both events occur together, and the probability that A or B occurs but not both.

How to Calculate the Probability of Events?

The simplest way to define probability is as the ratio between the number of favorable outcomes and the total number of possible outcomes.

The value of probability is always between 0 and 1. For ease of understanding, we often write probabilities as a percentage. You can represent the probability of an event as follows:

Probability of A: P(A),

Probability of B: P(B),

+: P(+),

Probability of ♥: P(♥), and so on.

Probability of a Specific Event – Drawing Any Ball From a Bag

Consider an example with colored balls. Suppose there are orange, green, and yellow balls in a bag. Event A is the action of selecting a random ball. We can define Ω as the set of all balls. The probability of the event Ω, which means selecting any ball, is equal to 1. The sum of all possible probabilities in the sample space is always 1.

Now let’s solve a slightly more difficult case – what is the probability of drawing an orange ball? To find it, count how many orange balls are in the bag and divide it by the total number of balls. You can apply the same method to yellow balls or any other color. You will quickly see that the higher the count of the color, the higher the probability of drawing it randomly from that bag.

How to Use the Probability Calculator?

To make full use of our calculator, follow these steps:

1.Define the Problem You Want to Solve.

Start by dividing your problem into two independent events.

2.Determine the Probability of Each Event.

Once you understand how to estimate the probability of an event, calculate and collect all the necessary values.

3.Enter the Percentage Probability of Each Event in the Designated Fields.

After entering the values, the calculator will immediately show the specific probabilities for six scenarios:

Both events occur;

At least one event occurs;

Exactly one event occurs;

Neither event occurs;

Only the first event does not occur; and

Only the second event does not occur.

You can also view all scenarios at once. In addition, the calculator allows you to check six more possibilities when considering multiple tests:

Event A always occurs;

Event A never occurs;

Event A does not occur at least once;

Event B always occurs;

Event B never occurs; and

Event B occurs at least once.

You can adjust the number of trials or any other value in the calculator, and the remaining fields will update automatically. This makes it easy to find out, for example, what probability event B must have in order to reach a 50% chance of both events occurring.

Conditional Probability

A key aspect of probability is understanding whether events are dependent or independent. Two events are independent if the outcome of the first does not affect the probability of the second. For example, when rolling a fair six-sided die, the probability of getting two ⚁ is 1/6, which is the same as getting four ⚃ or any other number.

Suppose you roll two dice and get five ⚄ on the first roll. The probability of getting two ⚁ on the second roll remains 1/6 because the events are independent.

Probability Distributions and Cumulative Distribution Functions
We can differentiate probability distributions into two types depending on whether the variables are discrete or continuous.

A discrete probability distribution describes the probability of countable, specific outcomes. An example is the binomial probability, which evaluates the chance of achieving a particular success in multiple trials, such as flipping a coin. In the Pascal distribution (or negative binomial), the number of successes is fixed, and you want to calculate the total number of trials required.

The Poisson distribution is another discrete probability distribution and represents a special case of the binomial distribution. You can calculate it using our Poisson distribution calculator. The probability mass function also defines a discrete probability distribution by assigning probabilities to individual outcomes. The geometric distribution serves as a classic example of using the probability mass function.

FAQs