Statistics/Distributions/Geometric
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Geometric Distribution refers to the probability of the number of times needed to do something until getting a desired result. For example:
- How many times will I throw a coin until it lands on heads?
- How many children will I have until I get a girl?
- How many cards will I draw from a pack until I get a Joker?
Just like the Bernoulli Distribution, the Geometric distribution has one controling parameter: The probability of success in any independent test.
If a random variable X is distributed with a Geometric Distribution with a parameter p we write its probability mass function as:
With a Geometric Distribution it is also pretty easy to calculate the probability of a "more than n times" case. The probability of failing to achieve the wanted result is 
.
Example: a student comes home from a party in the forest, in which interesting substances were consumed. The student is trying to find the key to his front door, out of a keychain with 10 different keys. What is the probability of the student succeeding in finding the right key in the 4th attempt?
