Question

Problem 7. A company aims to predict the likelihood of a flight arrival delay up to six hours before airlines notify passengers by crunching data on weather, a flight's prior inbound airplane's status, FAA updates, historical data and other information. Assume that 20% of all flights summer some kind of delay and that the company predicts as delayed 50% of the flights that are actually delayed, while it (wrongly) predicts as delayed 5% of the flights landing on time.

a) If you are taking three flights on three different days this summer, what is the probability that at least one of them is delayed? In case you needed to make any assumption, explain which.

b) What percentage of flights are announced to be delayed by the company?

c) If the company announces a delay at a given flight, what is the probability that it is actually delayed?

Answer 1

Let us define the events , .

Thegiven probabilities are

a) Thbe number of flights delayed follows Binomial distribution,

Here .

If you are taking three flights on three different days this summer, what is the probability that at least one of them is delayed is

We assume the delay of flights are independent of each other.

b) Using total probability thorem,

Thus of flights are announced to be delayed by the company.

c) Using conditional probability,