Geometric Vs Hypergeometric Distribution
Geometric Vs Hypergeometric Distribution
Geometric Distribution
The geometric distribution is used to model the number of trials needed until the first success occurs in a series of independent Bernoulli trials. In other words, it answers the question, “How many attempts do
we need to achieve a certain outcome?”
For example, imagine flipping a fair coin until you get heads. The geometric distribution can tell you the probability of getting heads on the first, second, third, or any specific trial. Each trial has two possible outcomes: success (getting heads) or failure (getting tails).
Hypergeometric Distribution
The hypergeometric distribution is used to model situations where you draw a sample from a finite population without replacement. It calculates the probability of obtaining a specific number of successes (objects of interest) in the sample.
To illustrate this, imagine you have a bag of colored balls: 10 red balls and 20 blue balls. If you randomly
draw 5 balls from the bag without replacement, the hypergeometric distribution can tell you the
probability of getting a certain number of red balls in the sample.
The main difference between the geometric and hypergeometric distributions lies in the nature of the events they model
Geometric distribution focuses on the number of trials needed until the first success, considering
repeated attempts at an independent event (like flipping a coin until heads appears).
Hypergeometric distribution focuses on the number of successes in a sample drawn without
replacement from a finite population (such as drawing balls from a bag without putting them back).
In summary, the geometric distribution deals with repeated trials until a specific outcome is achieved, while the hypergeometric distribution deals with drawing samples without replacement from a finite population.
