Geometric Distribution
Trials until the first success.
Key idea
Trials until the first success.
In depth
The number of trials until the first success: P(X = k) = (1 − p)ᵏ⁻¹p, mean 1/p. It is memoryless: the number of failures so far does not change future chances.
Worked example
Rolling a die until a six: p = 1/6, expected number of rolls = 6.
Formula
Real-world uses
- Estimating how many calls are needed before a successful sale or how many tries to pass a test
Common mistake
Mixing up counting trials (including the success) with counting failures only.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Geometric Distribution?
Trials until the first success. It is a topic at the expert level in Probability & Statistics.
What is the formula for Geometric Distribution?
The key formula is P(X=k) = (1−p)ᵏ⁻¹p.
Where is Geometric Distribution used in real life?
Real-world examples: Estimating how many calls are needed before a successful sale or how many tries to pass a test.
What should I learn before Geometric Distribution?
Make sure you are comfortable with Binomial Distribution, the previous topic in Probability & Statistics.
What is a common mistake with Geometric Distribution?
Mixing up counting trials (including the success) with counting failures only.
How can I practise Geometric Distribution?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Geometric Distribution?
Move on to Poisson Distribution next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- Residuals and R² – Error of a fit and proportion of variance explained.
- Simpson’s Paradox – A trend reverses when groups are combined.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Medical Tests and Base Rates – Why positive results can still be probably false.