Question

In: Statistics and Probability

American Airlines operates flights to a handful of destinations out of Oklahoma City’s Will Rogers World...

American Airlines operates flights to a handful of destinations out of Oklahoma City’s Will Rogers World Airport, but let’s think about three in particular: to Dallas, to Charlotte, and to Phoenix. The probability that the Dallas flight is full is 0.6 and assume probabilities of 0.5 and 0.4 for the other cities. Assume the events 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 not full?

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

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

Solutions

Expert Solution

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 is 0.4

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 not full?

the probability that at least one flight is not full is

ans: the probability that at least one flight is not full is 0.88

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

the probability that only the Charlotte flight is full is same as the probability that Charlotte flight is full and Dallas flight is 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 flights is full?

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

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

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

orchestra answered 1 year ago

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