Probability Calculator

Calculate probability based on the number of all possible outcomes and the number of favorable outcomes.

Result

Probability of Favorable Outcome:
Probability of Non-Favorable Outcome:

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How to Use

Our Probability Calculator is designed to assist you in calculating probability based on the number of all possible outcomes and the number of favorable  outcomes.

Enter the Total Number of Possible Outcomes: 

Begin by inputting the total number of possible outcomes for the given scenario. This represents the total number of ways an event could occur.

Enter the Number of Favorable Outcomes: 

Next, specify the number of outcomes you are interested in, i.e., the number of ways the favorable event can happen as per your criteria.

Click "Calculate": 

Once you've entered both values, click the "Calculate" button to obtain the probabilities.

View Results: 

The Probability Calculator provides you with two crucial results:

  • Probability of the Favorable Outcome: This represents the likelihood that the event you're interested in will occur.
  • Probability of the Non-Favorable Outcome: This is the probability that the event you're interested in will not occur.

 

Understanding Probability

Probability, often denoted as P, is a numerical measure of the likelihood of a particular event (X) occurring. The formula for calculating probability is:

P(X) =  Number of Favorable Outcomes / Total Possible Outcomes​

This formula essentially compares the number of possible successful outcomes to the total number of potential outcomes, providing a ratio that ranges from 0 to 1.

  • A probability of 0 indicates that the event is impossible.
  • A probability of 1 suggests the event is certain.
  • A probability between 0 and 1 represents the likelihood of the event happening.

The probability of an event occurring (X) and the probability of its complement (Xc) (not occurring) always add up to 1. Mathematically, this is expressed as:

P(X) + P(Xc)= 1

Therefore, the probability of the not favorable outcome P(Xc) can be calculated as: 

P(Xc) = 1 - P(X)

 

Example:

Let's consider a simple example involving the toss of a fair six-sided die. We want to calculate the probability of rolling a 4 and its complement, which is the probability of not rolling a 4.

Given:

  • Total Possible Outcomes (N): 6 (the six sides of the die)
  • Desired Outcome (X):  1 (rolling a 4)

Probability of Rolling a 4:
P(X) = X / N = 1 / 6 ≈ 0.1667

Probability of Not Rolling a 4:
P(Xc) = 1 - P(X)  = 1 - X / N = 1 - 1 / 6 = 5 / 6 ≈ 0.8333

This showcases how the probability of an event and its complement are complementary and cover all possible outcomes.