Question

A small regional carrier accepted 11 reservations for a particular flight with 10 seats. 7 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 40% chance, independently of each other.

a.) Find the probability that overbooking occurs.

b.) Find the probability that the flight has empty seats.

Answer 1

a)

The flight will be overbooked if out of passengers that are not regular all 4 will some to flight. The  probability that overbooking occurs is

Answer: 0.0256

b)

The flight will have empty seats if out of passengers that are not regular, less than 3 will be not come for flight. Here we need to use binomial distribution with parameters n=4 and p = 0.40. The probability that the flight has empty seats is

Answer: 0.8208