Problem 5. Trip to Grand Canyon
The second half of this class will be all about probability. To refresh your understanding of probability, we'll
work through a problem that only uses concepts from DSC 10.
Utkarsh is planning to go on a road trip to the Grand Canyon with his friends over the Memorial Day
weekend. Unfortunately, his friend Varun is worried about the fact that the air there might not be good for
his allergies.
The chances that the air is "good" on Friday, Saturday, and Sunday, in two different cities near the Grand
Canyon, are given below. The event that the air is good in Phoenix on Saturday depends on the event that
the air is good on Friday. All other events are independent.
City
Good on Friday
Las Vegas
1/3
Good on Saturday
2/5
Good on Sunday
3/8
Phoenix
1/4
3/4 if the air was good on Friday
5/9 otherwise
4/5
In all of the parts below, you may leave your answer unsimplified, as long as (1) it's possible to plug your
answer directly into a calculator to get the right answer, and (2) you show all of your work. So, an answer
like "1" is acceptable, but "1 minus the probability it is good on Sunday in Phoenix" is not.
a)
What is the probability that the air is good in both Las Vegas and Phoenix on Sunday?
b) What is the probability that the air is not good in Phoenix on Sunday, given that it was good
in Phoenix on both Friday and Saturday?
c) What is the probability that the air is not good in Phoenix on Saturday?
d) What is the probability that the air is good on exactly two of the three days in Las Vegas?
e) What is the probability that the air was good in Phoenix at least once over the three
days?