Prof Leighton arrives at an airport At the baggage carousel

Prof. Leighton arrives at an airport. At the baggage carousel, she discovers that her baggage is missing. The number of claims for missing baggage for the airline she has just travelled with is 8 per day.

(a) What is the probability that, on a given day, exactly 4 claims for that airline occur?

(b) How large is the probability of no claims in one day?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a)
The number of claims for missing baggage for the airline she has just travelled with is 8 per day
P( X = 4 ) = e ^-8 * 8^4 / 4! = 0.0573
b)
P( X = 0 ) = e ^-8 * 8^0 / 0! = 0.0003

It can be considered to Zero, we don\'t have existance of such occurence