Question

In 2017 there were 418 total motor vehicle crashes in Freedonia. Assuming that number reflects the true average now and that it follows the Poisson distribution, what are the odds 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. Round to four decimal places.

Answer 1

Mean number of accidents in 1 year = 418

So,

Mean number of accidents in 1 minute = 418/525600 = 0.0007953

P(at least one accident) = 1 - P(no accident)

P(no accident) = P(X=0) is given by:

So,

P(at least one accident) = 1 - 0.99920502 = 0.0007950

Odds that at least one accident will occur = P(at least one accident will occur)/P(at least one accident will not occur)

= 0.0007950/0.9992050 = 0..0008

So,

Answer is:

0.0008