Question

In 2018 there were 331691 total motor vehicle crashes in Freedonia. Assuming that number reflects the true average now and that it follows the Poisson distribution, what is the probability that at least one accident will occur somewhere in the state of Freedonia in the next minute? Hint: There 525,600 minutes in a year.

Answer 1

We have total number of crashes in a year, so first we will convert that into mean value by dividing the number with total number of minutes in a year

Mean = (331691)/(525600) = 0.6311 =

we have to find the probability that at least one accident will occur

So, P(at least 1) = 1- P(exactly 0) {total probability is always equal to 1}

where P(x=0) =

setting x = 0 and

we get

this gives us

or

We know that P(at least 1) = 1 - P(x=0)

setting the value of P(x = 0)

we get

P(at least 1) = 1 - 0.5320 = 0.4680

Therefore, required probability of at least one accident = 0.4680 (rounded to 4 decimals)