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Math 156–Sat: HW #3
Name:
1. A college library has four copies of a certain book; the copies are numbered 1, 2, 3, and 4. Two of
these books are randomly selected. The first selected book is placed on 2-hour reserve and the second
can be checked out overnight. (5 points each)
(a) Construct a tree diagram to display the 12 outcomes in the sample space.
(b) Let A denote the event that book 4 is chosen. What outcomes are in A and what is P(A)?
(c) Suppose that books 1 and 3 are first printings, whereas books 2 and 4 are second printings.
Let B denote the event that exactly one of the chosen books is a first printing. What
outcomes are in B and what is P(B)?
2. A Gallup poll in March 2001 asked 1005 American adults how the U.S. should deal with the current
energy situation: by more production, more conservation, or both? The results are shown below.
(5 points each)
Response
Number
More production
332
More conservation
563
Both
80
No Opinion
30
TOTAL
1005
(a) If a person is randomly selected from this group, what is the probability that this person
responded “more production”?
(b) If three people are randomly selected (with replacement) from this group, what is the
probability that the first and third responded “both” and the second had “no opinion”?
(c) If three people are randomly selected (with replacement) from this group, what is the
probability that none of the three answered “more conservation”?
3. You draw a card at random from a standard deck of 52 cards. Find the following probabilities.
(a) The card is a red ace.
(b) The card is an ace given that it is red.
(c) The card is red given that it is a heart.
(d) The card is a queen.
(e) The card is a queen given that it is a face card.
(5 each)
4. Consider the table below classifying a randomly selected group of 202 people by both gender and
political affiliation.
Democrat
Republican
Independent
Male
36
45
24
Female
48
33
16
A person is randomly selected from this group. Find the following probabilities.
(5 points each)
(a) P(person is female)
(b) P(person is male given that person is a Republican)
(c) P(person is a Republican given that the person is a male)
(d) P(person is an Independent)
(e) Is being female (in this group) independent of being a Democrat? Give statistical support.
5. Twenty percent of cars inspected have faulty pollution control systems. Define the discrete variable x
as the number out of the next three cars inspected that have faulty pollution control systems. Build a
probability distribution table for x. (10 points)
6. Let x denote the amount of gravel sold (in tons) during a randomly selected week at a particular sales
facility. Suppose that the density curve has height given by the formula below. (5 points each)
21  x  0  x  1
f x   
otherwise
0
(a) Graph this density function.
(b) Find Px  0.6 
(c) Find P0.25  x  0.8
(d) Find the probability that the gravel sold exceeds ½ ton.
(e) Find the probability that the gravel sold is no more than ¼ ton.
7. The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152
pounds. Suppose that the weights of all such animals can be described by a normal distribution with
standard deviation 84 pounds. Let x be the weight of a randomly selected yearling Angus steer. Find
the following. (5 points each)
(a) P(x > 1200)
(b) P(1000 < x < 1150)
(c) Which is more unusual, a steer weighing at most 1000 pounds or a steer weighing at least
1250 pounds)?
(d) What weight makes up the highest 15% of weights of all yearling Angus steers?
(e) What weight makes up the lowest 20% of weights of all yearling Angus steers?