Question

You are thinking about the things that can go wrong on your trip home over the Thanksgiving break. You have booked a flight with US-Scareways. You know that in 30 percent of the cases the company has canceled the flight you were on. Should such a thing occur, there would be no other air travel option home for you. As a backup. You friend Walter offered you a ride back. However, you know that Walter only has a seat in his car for you with an 80 percent probability. What is the probability of you making it home for the holidays?

Answer 1

The probability that the person reaches home for the holidays is 0.94.

Explanation:

A person wants to go home for Thanksgiving and he has booked a flight with US-Scareways.

It is provided that in 30 percent of the cases the company has canceled the flight you were on.

SO there is 70% chance of reaching home without any difficulties.

In case the flight is cancelled, then as a backup the person's friend Walter offers a ride home.

Walter also has a 80% chance of giving the ride. So there is 20% chance the person will not be able to reach hone if his flight gets cancelled.

Consider the tree diagram below.

The events are:

FC = flight is cancelled

FT = Flight is on time

H = reaches home

Compute the probability that the person reaches home as follows:

P (Reaching Home) = P (H|FC) × P (FC) + P (FT)

`=(0.80* 0.30) +0.70\\=0.24+0.70\\=0.94`

Thus, the probability that the person reaches home for the holidays is 0.94.