If an event happens 13 times per year Find the probability t

\"If an event happens 13 times per year. Find the probability the event happens more than once in the month of December.\"

Solution

This is an example of Poisson Probability Distribution, for which the probability of k events within a given period, where the mean number of events during this period is m, is
P(k) = m^k*exp(-m)/k!

Now December has 31 days.
The mean number of events during a december is m = 13x31/365 = 1.10411.
The probabilities of k=0 and k=1 events in December are
P(0) = 1*exp(-m)/1 = 0.3315 and
P(1) = m*exp(-m)/1 = m*P(0) = 0.3660.
The probability of the event occurring more than once in December is
P(k>1) = 1 - P(0) - P(1) = 0.3025.