Everything to Learn about Binomial Probability

Binomial Probability

Suppose you are playing a dice game. You need three of five dice for showing the result lower than or equal to the number 4. The two remaining dice should show higher numbers.

So, What Is Your Winning Probability?

A binomial probability calculator can solve this sample problem easily. You already have the number of events (equal to the number of dice, five it is). You also know the number of successes (should be 3) that you need. On this front, you can calculate the single success’s probability (probably 4 of 6, i.e., 0.667). This data will help you find your probability of winning the dice game.

The first success of the trial does not affect the probability of failure or success in the subsequent events. In the case of the dice game, the conditions can be met. Every time the player rolls the die, it constitutes an individual and independent event.

At times, you can get interested in the trial number that you require to achieve the outcome. For example, you can wonder the number of rolls of the die necessary prior to throwing the six thrice. Such questions can get addressed by using the related statistical solution in the name of the negative binomial distribution. The only thing that you need to ensure is to read the possible differences between the negative distribution and the positive one.

What Are the Formulae for Binomial Probability?

To find the binomial probability, you can make the right use of a binomial probability calculator. However, you need to understand the equation:

P(X=r) = nCr * pʳ * (1-p)ⁿ⁻ʳ


  • n: total event number
  • r: required success number
  • p: the probability of a single success
  • nCr: combinations of n and r
  • P(X=r): the exact number’s probability of success

So, these are the things you required learning about Binomial probability.