Question

An airline has set up an overbooking system for one of its flights in order to lower costs. Reservations can only be made through an agency or on the company's website. On this flight, the company charters (rents) a 200-seat aircraft and has sold 202 reservations. It is assumed that the number of customers arriving for boarding can be modeled by a random variable X which follows the binomial distribution with parameters n = 202 and p = 0.971. 1. Calculate the probability that all customers will show up for boarding. 2. Calculate the probability that only one customer among the 202 who booked does not show up for boarding. 3. Deduce the probability that the company is in a situation of overbooking (i.e., with more customers arriving for boarding than seats).

          An airline has set up an overbooking system for one of its flights in order to lower costs. Reservations can only be made through an agency or on the company's website. On this flight, the company charters (rents) a 200-seat aircraft and has sold 202 reservations. It is assumed that the number of customers arriving for boarding can be modeled by a random variable X which follows the binomial distribution with parameters n = 202 and p = 0.971.

1. Calculate the probability that all customers will show up for boarding.
2. Calculate the probability that only one customer among the 202 who booked does not show up for boarding.
3. Deduce the probability that the company is in a situation of overbooking (i.e., with more customers arriving for boarding than seats).

Added by Paul P.

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