Suppose that at an airport security checkpoint, 1 in 50 people are randomly selected for a search.

Question

Suppose that at an airport security checkpoint, 1 in 50 people are randomly selected for a search. If there are 33 people ahead of you in line, what is the probability that you will be the first one randomly selected to be searched?

Answer 1

1 in 50 people are randomly selected for a search

⇒ The probability of being selected for a search is p =1/50.

 

P {you are the first one in the line randomly selected}

   = P{33 people ahead of you in line not selected and you are selected}

   = (1-p)³³p

   = 0.010268.

 

Note: This is an application of the geometric distribution P{X = k) = (1-p)^k-1p