Question

Please find the answer, I kept getting wrong answer

A small regional carrier accepted 18 reservations for a particular flight with 15 seats. 14 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.)

A) Find the probability that overbooking occurs.     
B) Find the probability that the flight has empty seats.    

Answer 1

18 bookings were accepted, out of which 14 would be occupied.

Thus, 4 seats are remaining.

A.

Overbooking would occur if 2, 3, or 4 bookings happen.

We know that n=4.

p= 0.5

q= 0.5

Thus, we must find P(X=2),P(X=3) and P(X=4).

P(X=r)= nCr * p^r * q^n-r

Substituting the values in the equation,

P(X=2)= 0.375

P(X=3)= 0.25

P(X=4)= 0.0625

Thus, chance of overbooking

= 0.375 + 0.25 + 0.0625

= 0.6875

B.

The flight will have empty seats when 0 seats are booked, thus 1 seat will be left.

Thus, P(X=0)= 0.0625