Question

A small regional carrier accepted 13 reservations for a particular flight with 10 seats. 7 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 52% chance, independently of each other. Find the probability that overbooking occurs. Preview Find the probability that the flight has empty seats. Preview

Answer 1

Of the 13 booking, 7 are of regular customers who will show up. Of the remaining 6,

P(a person showing up), p = 0.52

q = 1 - p = 0.48

n = 6

Binomial distribution: P(X) = nCx p^x q^n-x

Number of seats remaining = 3

P(overbooking occurs) = P(X > 3)

= P(X = 4) + P(X = 5) + P(X = 6)

= 6C4x0.52⁴x0.48² + 6x0.52⁵x0.48 + 0.52⁶

= 0.3820

P(the flight has empty seats) = P(X < 3)

= P(X = 0) + P(X = 1) + P(X = 2)

= 0.48⁶ + 6x0.52x0.48⁵ + 6C2x0.52²x0.48⁴

= 0.3070