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.
$$ P(X=k) = (1-p)^{k-1}p $$
wherek 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 < ) means probability of less than failures before the first success. Similarly P(X > ) refers to probability of more than failures before the first success.
How to calculate
To calculate P(X < ), we need to sum all the probabilities from P(X = 0) through
P(X = ). See the details below.
Geometric Distribution Table
P(X < ) Important Points
- 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.
FAQs
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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