Geometric Distribution Calculator

Geometric Distribution Calculator


Number of Failures:
Probability of Success:


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  • How is Geometric Distribution Calculated?


    What is Geometric Distribution?

    If you wondered about the possibility of coming 5 times in a row when we throw a coin, the geometric distribution calculation tool can help. This article will also help you understand the geometric distribution formula and its definition.
    Geometric distribution describes the number of failures before a success. For example, let's assume that the dice are rolled until you get the number 6. The geometric distribution allows us to determine the probability of finding the number 6 in the first attempt, in the second or after.

    What is the Geometric Distribution Formula?

    Geometric distribution calculation formula;
    P = (1 - p) x x p.
    x → is the number of failures before the first success.
    p → an experiment is the probability of success.
    P → x is the geometric probability of success after failure.

    While calculating the geometric distribution probability, you can find the formulas of the units you can calculate with our calculation tool below.
    Mean → μ = (1-p) / p.
    Variance → σ² = (1-p) / p².
    Standard deviation is equal to → σ = √ [(1-p) / p²].

    Geometric Distribution Sample Question Solution?

    For example, let's move on the dice roll example. We will roll the dice until we get the result of 6. So how likely are we to get the number 6 at the end of the 2nd trial?
    • First, let's determine the probability of success for an experiment. For this example, the probability of success is equal to 1/6. (p = ⅙)
    • Calculate how many mistakes you will make before a success. According to our question, only one shot will fail to achieve success in the 2nd shot. (x = 1)
    • When we replace it in the formula, P = (1 - ⅙) 1 * ⅙ = will be 13.89%.

    Don't forget to check out more calculations about statistics!