Question

A small regional carrier accepted 12 reservations for a particular flight with 10 seats. 9 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 54% chance, independently of each other.

Find the probability that overbooking occurs.

Find the probability that the flight has empty seats.

Answer 1

Find the probability that overbooking occurs?

An overbooking will occur if 11,12 people show up. We know with 100% certainty that 9 people will show up, so the problem comes down to whether or not the 2 remaining people will show up.

We need to add the following probabilities:-

Here, p = 0.54 and q = 1 - p = 0.46

P(X=11) =

=

=  

P(X=12) =

=

=

P(X=11) + P(X=12) = 0.006284 + 0.000615 = 0.006899

0.69% is the probability that overbooking occurs.

Find the probability that the flight has empty seats.

P(X=0) =

=

0.042% is the probability that the flight has empty seats.