Question

Based on long experience, an airline found that about 2% of the people making reservations on a flight from miami to denver do not show up for the flight. suppose the airlines overbooks this flight by selling 261 ticket reservations for an airplane with only 255 seats.

Answer 1

Number of seats available = 255

Number of seats booked = 261

Probability of not showing up, p = 0.02

Probability of showing up, q = 1 - p = 1 - 0.02 = 0.98

Probability that more than 255 passenger showed up, P(X > 255) = P(256) + P(257) + P(258) + P(259) + P(260) + P(261)

= 261!/(256!* 5!) * 0.98^256 * 0.02^5 + 261!/(257!* 4!) * 0.98^257 * 0.02^4 + 261!/(258!* 3!) * 0.98^258 * 0.02^3 + 261!/(259!* 2!) * 0.98^259 * 0.02^2 + 261!/(260!* 1!) * 0.98^260 * 0.02^1 + 261!/(261!* 0!) * 0.98^261 * 0.02^0

= 0.1763 + 0.1681 + 0.1277 + 0.0725 + 0.0273 + 0.0051

= 0.5770