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, 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. 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.

Probability formula:

The formula for calculating probability is very simple.

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

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

$0.35+0.23+0.42$

$\text{Total probability} = 1$