# Poisson Distribution

The Poisson distribution is the probability distribution of independent event occurrences in an interval. If λ is the mean occurrence per interval, then the probability of having x occurrences within a given interval is:

#### Problem

If there are twelve cars crossing a bridge per minute on average, find the probability of having seventeen or more cars crossing the bridge in a particular minute.

#### Solution

The probability of having sixteen or less cars crossing the bridge in a particular minute is given by the function ppois.

Hence the probability of having seventeen or more cars crossing the bridge in a minute is in the upper tail of the probability density function.

#### Answer

If there are twelve cars crossing a bridge per minute on average, the probability of having seventeen or more cars crossing the bridge in a particular minute is 10.1%.