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

Step-by-step explanation:

(a)

7 persons will show up for sure, hence there is not any kind of probability here.

The other 5 persons have 50% chance to show up.

The flight will be overbooked, if either 4 will come or 5 will come.

From the total 5 persons, 4 can be chosen in ways.

The probability that any four among the 5 will come is .

The probability that all of the 5 passengers will come is .

Hence, the required probability is .

(b)

The probability that there will be exactly 10 passengers on the flight is .

The probability that there will be no empty seats in the plane is .

Hence, probability of having empty seats is .

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step-by-step explanation: