Question

A small regional carrier accepted 14 reservations for a particular flight with 13 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.
Find the probability that overbooking occurs.     
Find the probability that the flight has empty seats.

Answer 1

a )

A small regional carrier accepted 14 reservations for a particular flight with 13 seats.

8 reservations went to regular customers who will arrive for the flight.

Each of the remaining ( 14 - 8 = 6) passengers will arrive for the flight with a 56% chance

Let , x be the number of remaining passenger will arrive

x follows Binomial distribution with n = 6 and p = 56% = 0.56

Overbooking occurs if all 6 remaining passenger will arrive.

We have to find P( x = 6 )

Using Excel function , =BINOMDIST( x , n , p , 0 )

P( x = 6 ) =BINOMDIST(6 , 6 , 0.56, 0 ) = 0.0308

Probability that overbooking occurs is 0.0308

b)

The flight has empty seats if no more than 4 of the remaining 6 passenger will arrive.

We have to find P( x <= 4)

Using Excel function ,   =BINOMDIST( x , n , p , 1 )

P( x <= 4) =BINOMDIST(4 , 6 , 0.56, 1 ) = 0.8238

Probability that the flight has empty seats 0.8238