Question

[6.8] An airline has had 2 accidents in 50 years a) What is the probability that at least one accident will occur in a year? B) What is the probability of accidents occurring during the third year? C) Calculate the expected number of accidents per year d) Calculate the average time for an accident to occur

Answer 1

The average number of accidents given is 2 in 50 years. The number of accidents therefore could be modelled here as:

a) The probability here is computed as:

Therefore 0.0392 is the required probability here.

b) The probability of accidents occuring during the third year is computed as:

= Probability of one or more accident in a year ( due to memoryless property of poisson distribution )

= 0.0392 that is same as previous part

Therefore 0.0392 is the required probability here.

c) The expected number of accidents per year is equal to average number of accidents in a year that is 2/50 = 0.04

Therefore 0.04 is the expected value here.

d) The average time for an accident to occur is computed here as:

= 50/2 = 25 years

Therefore 25 years is the average waiting time.