Question

A small regional carrier accepted 13 reservations for a particular flight with 12 seats. 10 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 46% 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

Here we have,

A small regional carrier accepted 13 reservations for a particular flight with 12 seats. 10 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 46% chance, independently of each other

i.e. for remaining 2 seats there are 3 reservations and passenger will arrive for the flight independently with a 46% chance

Hence here

p=0.46 and n=3

This is Binomial Distribution with parameter n=3 and p=0.46

probability that overbooking occurs means all 3 passenger arrives for 2 seats, i.e.

Thus

probability that overbooking occurs is 0.0973

Now

the probability that the flight has empty seats means 0 or 1 passenger arrive for 2 seats i.e.

Thus

probability that the flight has empty seats is 0.5599