Question

Suppose instead that a flight has 58 seats and the likelihood of a person not showing up is 9%. The airline sells 62 tickets. a) What is the likelihood the flight is overbooked?

Answer 1

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P(arrive) = 1-P(not show up ) = 1-.09 = .91

The number of passengers arriving is X∼Binom(n=62,p=0.91).

The likelihood the flight is overbooked can be calculated as:

P(overbooked)

= P(more than 58 arrive)

= P(X>58)

= P(X=59) + P(X=60) + P(X=61) + P(X=62)

= 62C59* .91^59 * .09^3 + 62C60* .91^60 * .09^2 + 62C61* .91^61 * .09^1 + 62C62* .91^62 * .09^0

= 0.1797

Answer: 0.1797