Answer to Question #119469 in Statistics and Probability for Edem

Question

Suppose that an airline accepted 12 reservations for a commuter plane with 10 seats.
They know that 7 reservations went to regular commuters who will show up for sure.
The other 5 passengers will show up with a 50% chance, independently of each other.
Find the probability that the flight will be overbooked.

Answer 1

Find the probability that the flight will be overbooked.

P(X=4)+P(X=5)= C_5,4(0.5)⁴(1−0.5)⁵⁻⁴+C_5,5(0.5)⁵(1−0.5)⁵⁻⁵=(5+1)(0.5)⁵=0.1875