Math CentralQuandaries & Queries


Question from rougi, a teacher:

According to statistics of the company about 4% of the people who buy tickets do not arrive to the flight . The company sells 205 tickets to plane that has 200 places . Use the binomial distribution to calculate what is the probability that all the people who come to the flight get a place. thanks

Hi again Rougi,

Each ticket holder either shows up or doesn't. I am going to say that "success" is the event that the ticket holder doesn't show up. The probability of success p is then 0.04. Let X be the number of successes, that is the number of people who don't show up. If everyone who shows up gets a seat then X must be 5 or more. Thus you want

Pr(X ≥ 5) = 1 - Pr(x < 5).

Use the binomial distribution to find the probability that X is 0 or 1 or 2 or 3 or 4.


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