Probability Question

Question

According to an airline report roughly 1 piece of luggage out of every 200 that are checked are lost. Suppose that a frequently flying businesswoman will be checking 120 bags over the course of the next year. Approximate the probability that she will lose 2 or more pieces of luggage.

 

a) use the Binomial Probability Distribution

b)Use the Poisson Probability Distribution

Answer 1

Let L be the number of bags she loses.

 

L ∼ Bin(n = 120, p = 1/200)

 

The probability of losing 2 or more pieces of luggage is best computed using the complementary event. Also, you should use the approximation: (1 - 1/x)^rx → e^-r as r → ∞. Here we use r = 120/200 = 3/5.

 

P(L ≥ 2)

 

= 1 - P(L < 2)

 

= 1 - P(L = 0) - P(L = 1)

 

= 1 - C(120,0)(1/200)⁰(199/200)¹²⁰ - C(120,1)(1/200)¹(199/200)¹¹⁹

 

= 1 - (1 - 1/200)¹²⁰(1 + 120/199)

 

≈ 1 - e^-3/5(1 + 120/199)

 

≈ 0.12