Probability Calculator

This probability distribution calculator is used to find the chances of events occurring. You can calculate the probability for three types of events through this conditional probability calculator.

What is Probability?

In simple terms, 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. There are Multiple output probabilities in total which are generated as a probability chart after you input the values.

These include the Probability of A which is denoted by P(A). Similarly, there is P(B). The other values are A’, B’, (A ∩ B), (A ∪ B), and many others.

Formula of Probability Distribution Calculator

The probability calculator multiple events uses the following formula for calculating probability:

$\text{Probability} = \dfrac{\text{Event}}{\text{Outcomes}}$

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.

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.

How to Calculate Probability?

To understand how the values of events and outcomes are determined, let us consider a proper example.

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?

Solution

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:

$\text{Events} = 7$

The probability would be given as;

$\text{Probability of Peanuts} = \dfrac{7}{17}$

$\text{Probability of Peanuts} = 0.42$

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 heading, 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

$0.35+0.23+0.42$

$\text{Total probability} = 1$

$$

How to Find the Probability of A and B?

If you want to find the probability of two events, that are happening at the same time! Then we would say them to find the probability of A and B. There are several formulas to calculate the probability of A & B. It depends on the type of equation i.e. independent events or dependent events.

If you have an event and its probability is not affecting the other event, then it is called an independent event. If the event has such probability which is affecting on the other, then it is called the dependent event.

After recognizing the event type you can solve it with the following probability formulas:

Independent Event Formula:  p(A ∩ B)

Dependent Event Formula: p(A and B) = p(A) * p(B)

Or you can simply find the probability of a single, two or multiple events by using our Probability Calculator.

What are the Types of Probability?

There are three major types of probability in math.

• Theoretical Probability
• Experimental Probability
• Axiomatic Probability

What is Probability? Explain with an Example.

There are many branches of mathematics and probability is one of them. It measures the chances of a random event with different formulas, which depend on the situation and type of event. For example, if you tossed a coin in the air, the probability will be Head and Tail.

What is the Probability of an Event that is Impossible?

The answer is Zero Possibility. According to the definition of impossible events, the probability will remain zero if the possibility is zero. For example, if you tossed a coin in the air there is zero probability of the coin remaining in the air forever.

What Does a Probability of 0 Mean?

If you have an event that has 0 probability, it means that such event will not happen in any way. For example, if you tossed a coin in the air. There is a 0% chance of the coin staying in the air forever. It means the such event will never happen.

What are Probability Rules?

There are several rules of probability distribution calculator, here are a few basic rules:

If there are two events A and B, then:

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

P(A ∩ B) = P (B) ⋅ P (A | B)