MA 2621-BL01 Probability for Applications
B-Term Fall 2022 - Exam 01 (A)
Instructor: Nadeesha Jayaweera
First Name:.................................... Last Name:......................................
Section:
(Duration: 50 minutes)
Instructions:
ˆ Show all necessary work to get partial credits and follow directions.
ˆ You are allowed to use a calculator and one sheet (both-sided) of
notes.
GOOD LUCK...!!!
1. (10 points) Suppose 36% of families own a dog, 30% of families own a
cat, and 22% of the families that have a dog also have a cat. A family
is chosen at random.
(a) (5 points) Given that the family have a cat, find the probability
that they also own a dog.
(b) (5 points) Given that the family have a dog, find the probability
that they also own a cat.
2. (15 points) An oil exploration company currently has two active projects,
one in Asia and the other in Europe. Let A be the event that the
Asian project is successful and B be the event that the European
project is successful. Suppose that A and B are independent events
with P (A) = 0.4 and P (B) = 0.7.
(a) (10 points) What is the probability that at least one of the two
projects will be successful?
(b) (5 points) What is the probability of that neither Asian nor European projects will be successful?
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3. (20 points) A chemical supply company currently has in stock 100 lb
of a certain chemical, which it sells to customers in 5-lb batches. Let
X be the number of batches ordered by a randomly chosen customer,
and suppose that X has PMF,
X=x
1 2
3
4
5
P (X = x) k 0.4 0.3 0.05 0.15
(a) (5 points) Find the constant k, if the given distribution is a valid
PMF.
(b) (5 points) Calculate the expected value, E(X).
(c) (5 points) Calculate the variance, V ar(X).
(d) (5 points) Calculate the value of E(2X − 1).
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4. (15 points) A group of books consists of 4 STAT books and 7 MATH
books. In how many ways can a bundle of 5 books be selected if the
bundle has
(a) (5 points) any type of book (type does not matter)?
(b) (5 points) exactly 3 STAT books?
(c) (5 points) that at least 3 STAT books?
5. (10 points) How many different words (letter sequences) can be obtained by rearranging the letters in the word “INDEPENDENCE”?
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6. (15 points) Suppose that 20% of all copies of a particular textbook
fail a certain binding strength test. Let X denote the number among
8 randomly selected copies that fail the test.
(a) (5 points) Determine the probability distribution (PMF) of X.
(b) (5 points) Find the probability that exactly three copies fail
the test.
(c) (5 points) Find the probability that at most two copies fail the
test.
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7. (15 points) A customer help center receives on average 2.5 calls every
hour. Let X be the number of calls every year.
(a) (5 points) Find the probability distribution (PMF) of X.
(b) (5 points) What is the probability that it will receive, at least
two calls every hour?
(c) (5 points) What is the probability that it will receive, exactly
five calls every hour?
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8. (5 points) (BONUS Problem) How many times should a coin be
tossed so that the probability of getting at least one head is ≥ 99%?
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