Probability Calculator

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 Calculators.tech 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?

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 Calculators.tech.

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.

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.

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,
  
  $\text{Probability of } X = 0 is 0.25$
  
  $\text{Probability of } X = 1 is 0.5$
  
  Thus,
  
  $\text{Probability of } X \leq1 = 0.25 + 0.5$
  
  $\text{Probability of } X \leq1 = 0.75$

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.

FAQ's

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