Number of Failures:

Probability of Success:

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.

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].

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!