Avis Inc has reported that its fleet consists of 200000 vehi

Avis, Inc., has reported that its fleet consists of 200,000 vehicles. If the vehicles are independent in terms of accident incidence and each has a 0.99999 chance of making it through the year without being in a major accident, what is the probability that the entire fleet will avoid a major accident during the year?

Solution

Vehicles =200000

Prob for accident = 0.00001

As no of vehicles is very large, we can assume Poisson distribution

Mean = np = 2

probability that the entire fleet will avoid a major accident during the year

= Prob (no of accidents =0)

= 0.1353