Question

A small regional carrier accepted 23 reservations for a particular flight with 19 seats. 18 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 50% chance, independently of each other.(Report answers accurate to 4 decimal places.)Find the probability that overbooking occurs. Find the probability that the flight has empty seats.

Answer 1

We remove the 18 regular customers and their seats from consideration.

Thus, we consider the 23 - 18 remaining customers = 5; and 19 - 18 = 1 seat.

Overbooking means 3 or more of the 5 remaining passengers; each has a 50% chance remaining.

Overbooking = 1 - P(X ≤ 2) = 0.5

Probability of empty seats = P(X ≤ 1) = 0.1875