Probability Calculator

Probability calculator

Probability calculator evaluates the probability of occurring events out of total number of possible outcomes. This event probability calculator finds single-event probability. For example; a coin is tossed 90 times and we have to calculate the chances of occurring head in the 1^st five times.

What is probability?

Probability is simply how likely something is to happen. It is the outcome of a random event i.e. if we toss a coin we cannot say what will be the result whether it will be head or tail until the event happens. The probability ranges between 0 and 1.

If the probability of an event is 0.6 then it means there is a 60% chance of happening that event. The probability theory contains some sub-terms in it, to understand the concept of probability first we have to go through these basic terms.

• Experiment: To find well-defined outcomes we do experiments.
• Trial: The term “trial” represents how many times an experiment is performed.
• Outcome: It is the possible result.
• Sample space: All the possible results together make a sample space. It is represented by curly brackets {}.
• Event: The sample space is a set, and all of its subsets are known as events.

The formula of probability:

The general formula to calculate the single event probability is as follows:

Probability = number of events occurred n(E) / number of possible outcomes n(T)

How to calculate probability?

We can calculate the probability of a sample space by following the below steps.

• Check the number of all possible outcomes n(T)
• Find out the number of events that occurred n(E)
• Divide n(E) by n(T)

To understand the method more precisely, have a look at the following examples.

Example 1:

A fair die is rolled one time, what are the chances of coming the face 6?

Solution:

Step 1: Check the number of all possible outcomes n(T)

A die has six faces so n(T) = 6

Step 2: Find out the number of events that occurred n(E)

The die is rolled one time so n(E) = 1

Step 3: Calculation

Probability = n(E) / n(T)

Probability = 1/6

Probability = 0.1667

Probability = 16.67%

Frequently Asked Questions

1. What is the theoretical probability?

Theoretical probability is a way to predict the likelihood of an event occurring based on logical reasoning and analysis, without conducting any actual experiments. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

2. What is the experimental probability?

The probability is determined based on the results of an experiment repeated many times is an experimental probability.

3. What are the two requirements for a discrete probability distribution?

The two requirements for a discrete probability distribution are:

1. Each probability for possible outcomes must be between 0 and 1.
2. The sum of all probabilities must be equal to 1.

4. How to find probability with mean and standard deviation?

To calculate probability using mean and standard deviation, you can use the z-score formula:

P (X ≤ x) = Φ ((x – μ) / σ) and z = (x – μ) / σ.

In these formulas, Φ represents the cumulative distribution function (CDF), x is the value, μ is the mean, and σ is the standard deviation.

References

• Probability and statistics | Encyclopedia Britannica.
• Probability: The basics (article) | Khan Academy.