Q1 In a certain community, 42% of households have subscriptions for the cable television station
HBO. OF those households, 65% watch Game of Thrones which requires HBO. Overall, 70% of
the households watch baseball, but only 20% of the households that watch baseball also watch
Game of Thrones.
a) (10 points) Given that a household does NOT watch Game of Thrones, what is the
probability they do watch baseball?
b) (10 points) Given that a household does NOT watch baseball, what is the probability that
they have a subscription to HBO (HINT: Having HBO and watching baseball are
conditionally independent)?
Q2. There are two ums. The first urn is red and has N red balls, and the second urn is blue has M
blue balls. You take 3 balls from each urn, mix them up, and randomly place 3 balls back in
each urn.
a) (10 points) What is the probability you will now pull a blue ball out of the red umn
b) (10 points) If you pull a blue ball out of the red urn and do not replace it, what is the
probability you will pull a second blue ball out of the red urn?
Q3. Tom has been working at Acme Corporation for a year and is hoping to get a raise after his
first annual review. He can receive one of four different evaluations: Excellent, Above Average,
Acceptable, or Poor. He believes his probability of receiving each evaluation is 0.1, 0.5, 0.3, 0.1
respectively. He believes that if his evaluation is Excellent, he has a 90% chance of getting a
raise. If he gets Above Average, a 50% chance. If Acceptable, a 20% chance, and if Poor, only a
5% chance.
a) (5 points) If Tom gets a raise, what is the probability he received an Excellent evaluation?
b) (5 points) If Tom does not get the raise, what is the probability he received a Poor
evaluation?
c) (10 points) Tom is told that he did not receive a Poor evaluation. What probability does
he now have that he will get the raise?
Q4.Let Xbe a random variable with the following probability distribution:
1
1
1
f(-3)= 6
f(6) En
f(9) 3
a) (5 points) What is E[x]?
b) 5points) What is E[x2]?
c) (5 points) What is [(2x+1)2]?
d) (5 points) What is Var(2x+1)?
Q5.A chef works at a bistro restaurant which has an extensive and large list of toppings that they
provide on their burgers. On average, customers select five toppings. However, some customers
prefer their burger with fewer toppings and some customers want to add additional toppings.
a) (10 points) What is the probability that the chef will prepare a burger that has more than
five toppings?
b) 5points) What is the probability that 3 of the next 4 burgers the chef will prepare have
more than five toppings?
c) (5 points) What is the probability that the fifth burger the chef prepares will be the first
with more than 5 toppings?
Q6. Quality control is an important part of the manufacturing process. Factories need to ensure
that they are producing products that will function properly. One way of ensuring this is the case
is through random sampling. Suppose we know that, on average, 1 part in 1000 at the factory is
faulty. Each factory contains multiple machines that will work perfectly for a certain period of
time before they fail and require maintenance. The probability that a machine will fail during any
8-hour shift is 0.10.
a) (10 points) If 10,000 parts are selected at random and examined, what is the probability
that 6, 7, or 8 of the parts are faulty?
b) (10 points) What is the probability that a machine will operate at most 5 shifts before it
fails?

1.) Let X and Y be random variables that take on values x1, x2, …,...