Probability Calculator


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Probability of a Series of Events
Probability of A occuring 0 time(s) 0
Probability of A NOT occuring 0
Probability of A occuring 0
Probability of B occuring 0 time(s) 0
Probability of B NOT occuring 0
Probability of B occuring 0
Probability of A occuring 0 times and B occuring 0 times 0
Probability of neither A nor B occuring 0
Probability of both A and B occuring 0
Probability of A occuring 0 times but not B 0
Probability of B occuring 0 times but not A 0
Probability of A occuring but not B 0
Probability of B occuring but not A 0

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In simple terms, the probability is defined as the chance of getting a possible outcome. Consider that you have a dice and you have to determine the chance of getting 1 as the result. The probability of getting 1 would be 1/6. This is because the total outcomes are 6 and one side of the dice has 1 as the value. Determining probability involves various complex calculations. It is not like adding or subtracting two numbers. Accuracy is very important for users so you should use a top standard probability calculator for this purpose.

The Probability Calculator

It is important to use a quality calculator if you want the calculations to be completed without any mistakes being made. This probability calculator by is dependable in every manner and you can be sure that none of the results are incorrect. This is a concern for users who are calculating probability. There are various substandard calculators on the internet which should be avoided.

How to calculate probability on a calculator?

Stages of probability calculator

Here are the stages which the user has to complete to determine probability.

1. The input values which have to be entered

When the link of the calculator is opened, you would see the boxes for input values on the left. There are three input boxes and you need to enter the values for “number of possible outcomes”, “number of event occurs in A” and “number of event occurs in B”. Once these values have been entered, you can press the calculate button and advance to the next step.

2. The Output Values generated

There are 6 output values in total which are generated after the input values have been entered. These include Probability of A which is denoted by P(A). Similarly, there is P(B). The other values are A’, B’, (A ∩ B) and (A ∪ B)

Example of Probability

To understand how these values are determined, let us consider a proper example. Consider that the total number of outcomes is 10. The number of events occurred in A are 6 and The number of events occurred in B are 4. In addition to that, when these input values have been entered, you can advance to the interpretation of output values.

If the probability of A is taken as 6. The value of P (A’) would be 4. This is calculated by deducting the probability of A form the total probability which is taken as 1. Similarly, the other values would be determined by the calculator.

Main advantages of this probability calculator

There are several benefits of this calculator. Some of the key ones are listed below.

  • This calculator is completely free and users do not have to make any payments for using it. A lot of tools that apparently seem free have numerous conditions attached. For instance, the tool would be free for a limited span of time. When the time span has been completed, the user would not be able to use the calculator without making payments.
  • You can be absolutely sure that the data would not have any validity problems. It is dependable and you do not have to recheck anything. This calculator comes in handy for students, teachers as well as various other user types.
  • This calculator is an online tool so users can use it from multiple devices. There is no need to restrict to one device and download several soft wares to use this calculator. If you want, you can add it as a widget to the website as well. This is a good alternative for users who do not want to visit the website link every now and then.
  • When you talk about calculators for calculating probability or performing any other kind of calculation, the pace matters a lot. A lot of calculators are slow and users have to wait a long before results are produced. These problems are not present with this probability calculator by

How to Calculate the Probability?

The determination of probability is a stepwise process and users have to be aware of all stages. Here are all the steps which have to complete.

1. Choosing the correct event

The calculation of probability is initiated with the determination of an event. Every event has two possible outcomes. The first scenario is that it would take place and the second is that it would not. Consider that you have to determine the probability of having a Monday in one week. In other words, having Monday as the day of the week would be your event. In addition to that, the total number of days in a week is 7. Thus, the total number of outcomes would be 7.

2. Total number of outcomes

Total outcomes represent the maximum possible results that can be produced. For example, the total outcomes for a day of the week would be 7. This is simply because there are 7 days in a week.

3. Formula of Probability Calculation

The formula for calculating probability is very simple.

\(\text{Probability} = \dfrac{\text{Event}}{\text{Outcomes}}\)

To understand this formula in a better manner, we can go through another example. Consider that you have a bottle filled with 7 peanuts, 4 pistachios and 6 almonds. What is the probability that when you randomly pick one dry fruit, it would be a peanut?

We need to start by calculating the total outcomes. In this case, it would be given as

\(\text{Total Outcomes} = 7+4+6\)

\(\text{Total Outcomes} = 17\)

There are 7 peanuts in the bottle so the probability would be given as.

\(\text{Probability of Peanuts} = \dfrac{7}{17}\)

\(\text{Probability of Peanuts} = 0.42\)


4. Total Probability should be exactly 1

When you are calculating the probability of multiple events, make sure that the total probability is 1. To elaborate on this point, we can re-consider the example given above.

In the previous step, we calculated the probability of peanuts which was 0.41. Similarly, the probability of almonds and pistachios would be given as

\(\text{Probability of Pistachios} = \dfrac{4}{17}\)

\(\text{Probability of Pistachios} = 0.23\)

Similarly, the probability of almonds would be given as

\(\text{Probability of Almonds} = \dfrac{6}{17}\)

\(\text{Probability of Almonds} = 0.35\)

Hence, the total probability would be given as


\(\text{Total probability} = 1\)

Conditional Probability

In simple terms, conditional probability refers to the occurrence of one event provided that the other has occurred. Consider that there are two events A and B. Event A occurs before event B. Hence, the conditional probability would be the probability of event B provided that event A has already occurred.

Detailed Example

Consider that there is a bad full of 6 red balls and 6 green balls. If a person takes out one red ball, it would be counted as the first event. After that, if another red ball has been taken out, the probability of this event would depend on the first event. Let us further elaborate on this example.

  • When the first red ball is taken out, the probability would be 6/12.
  • In the second event when conditional probability would be applied, there would be 5 red balls. Thus, the probability would be 5/11. This output would be dependent on the first red ball taken out.

Conditional probability formula

The formula of conditional probability for the events A and B would be given as

\(P(A \mid B) = \dfrac{P(A \bigcap B)}{P(B)}\text{where} P(B)>\Theta \)

Interpretation of formula

In the above formula, conditional probability is the ratio of the probability of A intersection B and probability of B. However, an important condition in this relation is that probability of B should be greater than zero. In other cases, this formula does not hold validity.

Probability Distribution and Cumulative Probability Distribution

When you talk about probability distribution and cumulative probability distribution, they are both terms defining statistical outputs. There are obviously differences between the two terms. By going through the following points, you would be able to determine the difference between the two terms and understand the implications that each one of them has.

  • Probability distribution does not involve a range of values. Instead, the possible outcomes are determined for a specific value. As it is a distribution, the results are elaborated in the form of a table. Consider that you are flipping two coins at the same time. What would be the probability that you can get a tail? The outcome would be represented by random Variable X. The possible outcomes of both coins can be

    Coin 1 is head and Coin 2 is head
    Coin 1 is head and Coin 2 is tail
    Coin 1 is tail and coin 2 is head
    Coin 1 is tail and coin 2 is tail

    If you represent the data given above in tabular form, it would be given as follows
    0 0.25
    1 0.5
    2 0.25
  • If you have a look at the results mentioned above, the interpretation will be that there is 25% probability of getting no tails, 50% probability of getting one tail only and 25% probability of getting two tails. This is how you can determine the probability distribution.

  • Cumulative probability distribution does not involve a specific value but covers a range instead. We can get more understanding if we re-consider the example mentioned above. In the case of cumulative probability, the calculation is done for a range of values. If you want to know about the chances of getting one or fewer tails, it is an example of a cumulative probability distribution. Thus, the cumulative probability would be given as

    Probability of X \(\leq\)  1 = Probability of X = 0 + Probability of X = 1.

    Considering the above example,

    \(\text{Probability of } X = 0 is 0.25\)

    \(\text{Probability of } X = 1 is 0.5\)


    \(\text{Probability of } X \leq1 = 0.25 + 0.5\)

    \(\text{Probability of } X \leq1 = 0.75\)

Difference between theoretical and experimental probability

When you talk about the difference between theoretical and experimental probability, the theoretical probability is based on expectations. It is based on estimations and assumptions. On the other hand, the experimental probability is the actual set of results produced after the calculations have been completed. Experimental probability is not based on assumptions.

Further elaboration is explained through the following points.

  • Consider that you have to toss a coin for 10 times. What is the probability that you would get heads? On the basis of assumptions, you would expect that fifty percent of the outcomes would be headed. This is called theoretical probability.
  • If you perform an actual experiment and toss the coin 20 times, the outcome may be different. For instance, you may get 12 heads and 8 tails. In other words, experimental probability produces actual results and no predictions or assumptions are involved in this case.

Union of A and B

When you talk about A and B, they are taken as two sets. Let us consider an example so that better understanding is gained.

\(\text{Set A} = (2,5,6,7)\)

\(\text{Set B} = (2,6,8,9)\)

The union of A and B would include all elements that are present in both sets.

If the above example is considered, the union would be given as \(A U B = (2,5,6,7,8,9)\). This calculation clearly shows that all the elements of set A and B have been included in the union.

It is very common to make mistakes when statistical calculations are being performed. Hence, you should use an online calculator to avoid all kinds of errors. When you talk about the union of two sets, it would include all values that are present in both sets. In other words, it would be a combination of all values. The probability distribution is related to one value carried by the variable X. The user does not have to relate the variable to any range of values.

Conditional probability requires a particular event to occur before the probability has been calculated. For instance, if an event A occurs, the probability that event B would occur would be determined.


What are the 5 rules of probability?

Answer: 5 rules are following

  1. Rule 1: The probability of Any event (A) always between 0 and 1. (For any event A, 0 ≤ P(A) ≤ 1).
  2. Rule 2: The sum of the probabilities of all possible outcomes is equal to 1
  3. Rule 3: The Complement Rule
  4. Rule 4: Addition Rule for Disjoint Events
  5. Rule 5: Calculate P(A and B) using Logic

What are the 3 types of probability?

Answer: 3 types are following

  1. Classical Probability
  2. Relative Frequency Definition
  3. Subjective Probability

How many probability rules are there?

Answer: There are 3 basic rules for probability

How do you calculate the probability of multiple events?

Answer: Use our Calculator it is very simple and accurate