Final answer:
The probability of overbooking can be calculated using the binomial probability formula. In this case, the probability is 0.596 or 59.6%.
Step-by-step explanation:
To find the probability of overbooking for the small regional carrier, we need to calculate the probability that more than 14 passengers arrive for the flight.
We know that 13 reservations went to regular customers who will definitely arrive for the flight. This means we need to calculate the probability that at least 2 of the remaining 4 passengers will arrive for the flight.
Since each passenger has a 57% chance of arriving for the flight, the probability of a passenger not arriving is 1 - 0.57 = 0.43.
The probability of at least 2 passengers arriving can be calculated using the binomial probability formula:
P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)
P(X = 0) = (0.43)^4 = 0.0369
P(X = 1) = 4C1 * (0.43)^1 * (0.57)^3 = 0.3671
P(X ≥ 2) = 1 - 0.0369 - 0.3671 = 0.596
Therefore, the probability of overbooking is 0.596, or 59.6%.