# American Airlines operates fli

American Airlines operates flights to a handful of destinationsout of Oklahoma City’s Will Rogers World Airport, but let’s thinkabout three in particular: to Dallas, to Charlotte, and to Phoenix.The probability that the Dallas flight is full is 0.6 and assumeprobabilities of 0.5 and 0.4 for the other cities. Assume theevents that the flights to those destinations are independent.

a. What is the probability that all three flights are full?

b. What is the probability that at least one flight is notfull?

c. What is the probability that only the Charlotte flight isfull?

d. What is the probability that exactly one of the three flightsis full?

Answer:

Let

- DF=event that the Dallas flight is full
- CF=event that the Charlotte flight is full
- PF=event that the Phoenix flight is full

We know the following

The probability that the Dallas flight is full is 0.6

The probability that the Charlotte flight is full is 0.5

The probability that the Phoenix flight is full is0.4

We also know that the events DF,CF,PF are independent.

a. What is the probability that all three flights are full?

the probability that all three flights are full is

ans: the probability that all three flights are full is 0.12

b. What is the probability that at least one flight is notfull?

the probability that at least one flight is not full is

ans: the probability that at least one flight is not full is0.88

c. What is the probability that only the Charlotte flight isfull?

the probability that only the Charlotte flight is full is sameas the probability that Charlotte flight is full and Dallas flightis not full and Phoenix flight is not full

ans: the probability that only the Charlotte flight is 0.12

d. What is the probability that exactly one of the three flightsis full?

the probability that exactly one of the three flights is full issame as

the probability that Dallas is full and Charlotte and Phoenixare not full or Charlotte is full and Dallas and Phoenix are notfull or Phoenix is full and Charlotte and Dallas are not full

ans: the probability that exactly one of the three flights isfull is 0.38