Question 1134959: A small regional carrier accepted 16 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 48% chance, independently of each other.
A) Find the probability that overbooking occurs.
B) Find the probability that the flight has empty seats.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! empty seats mean that no more than 3 of the other 8 will arrive for the flight.
probability of 3 arriving is 8C3*0.48^3*0.52^5=0.2355
probability of 2 arriving is then 0.1275
probability of 1 is 0.0395
probability of 0 is 0.0053
That sum is 0.4078 ANSWER B
overbooking is 5,6,7,8.
do just 4, even though this isn't asked for
probability is 70*0.48^4*0.52^4=0.2717
This plus the 0.4078 is 0.6795
That is the probability no overbooking will occur. The probability that overbooking will occur is the complement of 0.3205 ANWER A
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