A geometric distribution can be defined as the probability of experiencing the number of failures before you get the first success in a series of Bernoulli trials. Bernoulli trials refer to two possible outcomes for each trial (success or failure). For example : What's the probability that we have to face 4 failures before we get heads on a coin.

$$ P(X=k) = (1-p)^{k-1}p $$

where `k`

is the number of trials. `k-1`

can be read as the number of failures prior to the first success. `p`

is the probability of success on each trial.

Solution

`P(X < ) `

- Probability of success must lie between 0 and 1.
- Number of trials can't be less than or equal to 0. It must be a whole number, can't be in decimals.

Geometric Distribution has the following properties -

- Each trial has only two possible outcomes - success or failure.
- The probability of a success on any trial is same.
- Trials are independent.

Both have the same properties but they are different in terms of objective. In a binomial distribution, the number of trials is fixed. Whereas when we use a geometric distribution, we are interested in the number of trials required until we get success.

- Suppose you work as a operational manager in a factory and want to know the probability that the kth product on a production line is defective
- As a marketing lead, it is expected from you to calculate the number of trials required before sale turn out to be a success

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