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**Education Calculators** ▶ Probability Calculator

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The probability calculator is the smart tool that helps to calculate a probability for a single event, multiple events, two events, for a series of events, and also conditional probability events. If you want to calculate the probability of a and b and for any number of events, then the above calculator for probability will work best for you!

Well, come to the point; simply give a read to this post to know how to calculate probability, different probability equations, all probability formula’s, statistics probability calculator, and much more you need to know about probability.

So, let start with the best definition of probability!

Probability is said to be as the likelihood of an event or more than one event occurring. Probability is something that indicates the possibility of acquiring a certain outcome and can be calculated by using a simple probability formula.

The origin of the probability theory begins from the study of games such as dice, tossing coins, cards, etc. But, nowadays, probability has great importance in decision making. The Classical Theory depicts that probability is the ratio of the favorable case to the total number of equally likely cases. The subjective approach reveals that the probability of an event is assigned by an individual on the basis of the evidence available to him/her.

The idea of probability as a useful science is accredited to a well-known French mathematicians Blaise Pascal and Pierre de Fermat.

According to the Calculus, Volume II by Tom M. Apostol, both Blaise Pascal and Pierre de Fermat were solving a gambling problem in 1954. They works best in finding out the number of turns needed to obtain a 6 while rolling 2 dices. Yes, the discussions from Pascal and de Fermat’s laid out the groundwork for the concept of probability theory.

The formula of the probability of an event is as follow:

**P (A) = Number of Favorable Outcome / Total Number of Favorable Outcomes**

Or, Probability formula is:

**P(A) = n(E)/n(S)**

Where,

- P(A) is said to be as the probability of an event ‘A’
- n(E) is said to be as the number of favorable outcome
- n(S) is said to be as the number of events in the sample place

Note: Here, the favorable outcome is indicated as the outcome of interest.

Now, let’s take a look at the basic probability formulas!

Swipe down!

0 ≤ P(A) ≤ 1

P(A∪B) = P(A) + P(B) – P(A∩B)

P(A’) + P(A) = 1

P(A∩B) = 0

P(A∩B) = P(A) ⋅ P(B)

P(A | B) = P(A∩B) / P(B)

P(A | B) = P(B | A) ⋅ P(A) / P(B)

Well, come to the point, calculating probability notation becomes easy with the ease of statistic events or conditional probability calculator.

The probability calculator is an advanced tool that allows you to find out the probability of single event, multiple events, two events, and for a series of events. Also, this calculator works as a conditional probability calculator as it helps to calculate conditional probability of the given input. In short, finding probability becomes easy with the ease of this probability events calculator. Apart from probability equation, you can readily find probability with this calculator for probability.

Well, you can readily calculate conditional or probability for events with this probability events calculator as it is loaded with the user-friendly interface, it is 100% free to do probability calculations. Read on!

**Input:**

- First of all, you have to choose the ‘Single Probability’ option form the drop-down menu of calculator
- Very next, you have to enter the number of possible outcomes into the designated field
- Now, you have to enter number of events occurred (n)A into the designated field

**Output:**

Once done, hit the calculate button, this calculator for single event probability will generate:

- Probability of event that occurs P(A) in both decimal and percentage
- Probability of event that does not occurs P(A’) in both decimal and percentage

**Input:**

- First of all, you have to choose the ‘Multiple Events Probability’ option form the drop-down menu of this probability calculator for multiple events
- Right after, you have to enter the number of events occurs (n)A into the given inputs
- Very next, you have to enter the number of events occurs (n)B into the designated field of this calculator

**Output:**

Once you entered all the above parameters, hit the calculate button, then this calculator for multiple events probability will generate:

- Probability of event that occurs P(A) in both decimal and percentage
- Probability of event that does not occurs P(A’) in both decimal and percentage
- Probability of event B occurring P(B) in both decimal and percentage
- Probability of event B not occurring P(B’) in both decimal and percentage
- Probability of both events occurring P(A ∩ B) in both decimal and percentage
- Probability of either events occurring P(A ∪ B) in both decimal and percentage
- Conditional Probability P(A | B) in both decimal and percentage

**Input:**

- First, you have to choose the option ‘Probability of Two Events’ from the drop-down menu of this probability of two events calculator
- Very next, you have to select the input format whether you want to add the values in decimal or percent
- Right after, you have to add the value of Probability of P(A) into the designated box
- Then, you have to add the value of Probability of P(B) into the designated box

**Output:**

Once you added all the values into the given fields, hit the calculate button, the probability of two events calculator will generate:

- Probability of event that does not occurs P(A’)
- Probability of event B not occurring P(B’)
- Probability of both events occurring P(A ∩ B)
- Probability of either events occurring P(A ∪ B)
- Probability that A or B occurs but not both P(AΔB)
- Probability of neither A nor B occurring P((A∪B)’)
- Probability of B occurring but not A

The calculator will show all the above values in both decimal and percentage

**Input:**

- First of all, you have to choose the option “Probability of a Series of Events” from the designated field of this Probability of a Series of Events calculator
- Very next, you have to enter the value of probability and number of repeat times for a ‘Event A’ into the designated field
- Right after, you have to add the value of probability and number of repeat times for a ‘Event B’ into the given field

**Output:**

Once you entered all the values into the designated fields, simply hit the calculate button, this probability will instantly generate the following results:

- Probability of A occurring 2 times
- Probability of A not occurring
- Probability of A occurring
- Probability of B occurring 4 times
- Probability of B not occurring
- Probability of B occurring
- Probability of A occurring 2 times and B occurring 4 times
- Probability of neither A nor B occurring
- Probability of both A and B occurring
- Probability of A occurring 2 times but not B
- Probability of B occurring 4 times but not A
- Probability of A occurring but not B
- Probability of A occurring but not B

**Input:**

- First of all, you have to select the option “Conditional Probability P(A | B)” from the designated field of this conditional probability calculator
- Very next, you have to enter the value of the probability a and b into the designated field
- Then, you have to enter the value of probability P(B) into the designated field

**Output:**

Once done, then simply hit the calculate button, the conditional probability calculator will generate:

- Conditional Probability P(A | B) in both decimal and percentage

Thankfully, how to find probability of a and b becomes easy with the assistance of this calculator for conditional probability.

Give a read to know about the different types of probability events:

If the event E contains only one sample point of a sample space, it is said to be as a simple event or an Elementary Event. Remember that it is an event, which only contains exactly one outcome.

Example of single event probability:

Suppose that you throw a die, the possibility of 2 appearing on the die is said to be a simple event and is given be E = {2}.

If there is more than one sample point on a sample space, then this is said to be as a compound event. This event indulges combining of two or more events together and determining the probability of such a combination of events.

Example of compound event in probability:

When you throw a die, there is the possibility of an even number appearing is said to be a compound event, as there is more than one possibility, there are three possibilities that are E = {2,4,6}.

A certain event is said to be an event which is sure to occur in any given experiment. The probability of such type of event is said to be 1.

When an event cannot occur, means there is no chance of the event occurring, then this is said to be an impossible event. The probability of an impossible event is referred to as 0.

Example of impossible event in probability:

The card you drew from a deck is both red and black is said to be an impossible event.

If the outcomes of an experiment are equally likely to happen, then they are said to be as equally likely events.

Example of equally likely events in probability:

When you toss a coin, you are equally likely to attain heads or tails.

For an event E the non- occurrence of the event is said to be its complimentary event. Generally, the complimentary events are said to be the events that cannot occur at the same time.

Example of Complimentary Events in probability:

When a die is thrown, attaining an odd face and an even face are said to be complementary events.

Two events are referred to as the mutually exclusive probability events when both cannot occur at the same time. Remember that mutually exclusive probability events always have a different outcome. Two simple events are always said to be a mutually exclusive, whereas two compound events may or may not be!

If A and B are two events, then;

( A ∩ B ) = Ø

and,

Intersection probability

P ( A ∩ B ) = 0

Union probability

P ( A ∪ B) = P ( A ) + P ( B )

Let we describe both terms in simple words:

- Dependent probability events are connected to each other
- Independent probability events aren’t connected, means the probability of one happening has no impact on the other

Here, the probability equation you use is slightly different.

**P(A and B) = P(A) • P(B|A)**

Where;

- P(B|A) just indicated as “the probability of B, once A has happened)

**Sample Problem:**

If 85% of employees have health insurance, out of 85%, only 45% had deductibles higher than $1,000. So, what percentage of individuals had deductibles higher than $1,000?

**Step # 1:**

- You have to convert your percentages of the two events to decimals, let’s take a look at the example

85% = .85.

45% = .45.

**Step # 2:**

- Now, you have to multiply the decimals from step 1 together

.85 x .45 = .3825 or 38.35 percent.

So, the probability of individuals having a deductible of over $1,000 is 38.35%

That’s how to calculate probability of two events occurring together!

All you need to use the specific multiplication rule formula. You ought to multiply the probability of the first event by the second. For instance, if the probability of event A 2/9 and the event B is 3/9, then the probability of both events are happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.

**Sample Problem:**

The chances of getting a job you applied for are 45% and the chances of getting the apartment you applied for are 75%, then what about the probability of you getting both the new job and the new apartment?

**Step # 1:**

- You ought to convert your percentages of the two events to decimals, let’s take a look from the above example

45% = .45.

75% = .75.

**Step # 2:**

- Now, you have to multiply the decimals from the step 2 together:

.45 x .65 = .3375 or 33.75 percent.

So, the probability of you getting the job and the apartment is 33.75%

The probability of A and B means that you want to know the probability of two events that happening at the same time. There are different formulas that entirely depending on if you have dependent events or independent events.

**Formula for the probability of A and B (independent events): p(A and B) = p(A) * p(B)**

Remember that if the probability of one event doesn’t affect the other, then it means you have an independent event. So, as mentioned earlier all you need to multiply the probability of one by the probability of another.

**Formula for the probability of A and B (dependent events): p(A and B) = p(A) * p(B|A)**

Apart from these probabilities equations, you can simply add the parameters into the above probability calculator to find the probability of events.

Apart from the probability equations, you can simply add the parameters into the above probability calculator to find the probability of events. But, if you want to calculate probability manually, then give a read!

All you need to follow the given steps to calculate probability:

- First of all, you have to determine a single event with a single outcome
- Then, you ought to identify the total number of outcomes that can occur
- Very next, you have to divide the number of events by the number of possible outcomes

Let’s digging deeper!

The first step to do probability calculation is to find out the probability that you want to calculate. This can be indicated as an event, suppose that the probability of rainy weather, or rolling a specific number on a die. The event must have at least one possible outcome. For instance, if you want to find the probability of rolling a three with a die on the first roll, you would figure out that there is a possible outcome: means you either roll a three or you do no roll a three.

Very next, you ought to determine the number of outcomes that can occur from the event that you identified from step one. If we talk about the example of rolling a die, there can be 6 total outcomes that can occur as there are 6 numbers on a die. So, it’s clear that for one event – rolling a three, that can be 6 different outcomes that can occur.

Once you determined the probability event along with its corresponding outcomes, you have to divide the total number of events by the total number of possible outcomes. For instance, rolling a die once and landing on a three can be considered probability of one event. So, you can continue to roll die – hence, each time you roll would be said as a single event.

So, from the above example, the results in a fraction: 1/6.

Want to calculate probability with multiple events instantly, then simply probability calculator for multiple events. No doubt, calculating probability with multiple random events is quite similar to calculating probability with a single event, however, there are only few additional steps to stick to reach a final solution. The below steps highlight how to calculate the probability of multiple events:

- First of all, you have to determine each event that you will calculate
- Very next, you have to calculate the probability of each event
- Finally, you have to multiply all probabilities together

If you want to calculate a probability as a percentage, you ought to solve the problem as you normally would, means, you have to convert your answer into a percent.

**For example;**

If the number of desired outcomes divided by number of possible events that is .25, then you ought to multiply the answer by 100 to get 25%. If there is a odds of a particular outcome in percent form, then simply you have to divide the percentage by 100 and now multiply it by the number of events to calculate the probability.

All you need to enter the values into the above-given fields, the calculator for probability does all for you within a couple of seconds.

The three types of probability are as follow:

- Classical
- Relative Frequency Definition
- Subjective Probability

**Basic Rules of Probability:**

- Probability Rule One – (For any event A, 0 ≤ P(A) ≤ 1)
- Probability Rule Two – (The sum of the probabilities of all possible outcomes is said to be 1)
- Probability Rule Three – (The Complement Rule)

Probabilities Involving Multiple Events:

- Probability Rule Four – (Addition Rule for Disjoint Events)

Finding P(A and B) using Logic:

- Probability Rule Five – (The General Addition Rule)

Remember it all based on the range of the random number generator. For instance, if the range is 1 through 9, then the probability of getting a specific number is said to be as 1/9

There is a 66.5 percent chance of it landing on a 6 at least once.

Then, your answer would be 1/6, or approximately 17%.

2/6, once the die tossed, the odds to get 1 is 1/6 or to get 2 is also said to be 1/6. Thus, 1/6 + 1/6=2/6 or 1/3 or 0.333.

Really, you can’t. The thing only that you can go off of is their skill. Remember that the players are human too, and they might have a bad day, means they don’t play as well as they usually do!

These are the real-life examples of probability:

- Weather Forecasting
- Batting Average in Cricket
- Politics
- Flipping a coin or Dice
- Insurance
- Are you likely to die in an accident
- Lottery Tickets
- Playing cards

Remember that probability is something that provides you with information about the likelihood that something will happen. So, simply account the above probability calculator to figure out the probability for events or according to condition!

From Wikipedia, the free encyclopedia – Probability Interpretations & Theory – Summary of probabilities – Probability chart – Relation to randomness and probability in quantum mechanics

From the source of wikihow – By the trained team of editors and researchers – How to Calculate Probability (4 different ways) – Finding the Probability of a Single Random Event – Calculating the Probability of Multiple Random Events – Converting Odds to Probabilities – FAQ’s

From the source of study – Chapter 22 / Lesson 6 – Transcript | Additional Activities – Expert Contributor – Probability Rules – The Addition Rule – The Multiplication Rule – The Complement Rule – Law of Total Probability – Along Calculations of Probability

The authorized source of mathsisfun – provided with Probability: Types of Events – statistics data – explore all about probability from this platform!