"A small regional carrier accepted 14 reservations for a particular flight with 12 seats. 8 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 56% chance, independently of each other."

a. Find the probability that overbooking occurs.
b. Find the probability that the flight has empty seats.

a.  0.1762

b.  0.5381

Step-by-step explanation:

If 8 of the 14 reservations are regulars customers, there are just 6 reservations with the possibility to arrive or not for the flight. Additionally, there are just 4 free seats for the 6 reservations.

Now, the probability that x customers arrive for the flight follows a Binomial distribution, so it is calculated as:

Where p is probability that a customer arrive, so it is equal to 0.56 and n is the total number of customers with the possibility to arrive or not, in this case it is 6. Replacing values we get:

So, the probability that a overbooking occurs is the probability that 5 or more customers from the 6 arrive for the flight and the probability that the flight has empty seats is the probability that 3 or less customers from the 6 arrive for the flight.

Then, the probability that overbooking occurs is:

At the same way, the probability that the flight has empty seats is:

-7/8

step-by-step explanation:

instead of subtracting you add the -6/8 and -1/8