Question

A small regional carrier accepted 17 reservations for a particular flight with 15 seats. 13 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 51% 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

Given,

A small regional carrier accepted 17 reservations having 15 seats.

13 regular customers who will surely arrive for the flight.

The remaining passengers will arrive for the flight with a 51% chance.

Let X= number of the remaining passengers those arrive.

X follows a binomial distribution with probability p= 51%=0.51 and n= (17-13)=4

1. Overbooking occurs when more than 2 non-regular passengers will arrive for the flight, so the probability of overbooking occurs is P(X> 2)

  

2. The flight will have empty seats if less than 2 non-regular passengers will arrive for the flight, so the probability that the flight has empty seats P(X< 2)