Airlines strategically overbook flights, not due to error, but as a calculated risk based on data science to maximize profit. By selling more tickets than available seats, airlines leverage historical data to predict passenger no-shows.

Using binomial distribution, which models independent events with binary outcomes and a fixed probability of success (here, 95% passenger show-up rate), airlines can calculate the probability of overbooking. For a flight with 304 tickets sold on 300 seats, the probability of overbooking (301+ passengers showing up) is approximately 0.014%.

The expected value of overbooked passengers, calculated by weighing each outcome by its probability, helps quantify the long-term average of overbooked situations. While the expected number of overbooked passengers might be low, the potential financial gain is substantial. For instance, selling just 4 extra tickets on 10,000 flights could generate $8 million in additional revenue, with compensation costs for bumped passengers being significantly less, around $5,000.