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Math 30011
Kent State University – Stark Campus
Spring 2009 – March 18, 2009 – Dr. Kasturiarachi
Basic Probability & Statistics
Lab #2: Probability
NAME:
PARTNER:
In this Lab we will explore the concepts of probability in several different ways.
The first Activity #1 uses a two-way table to find probabilities of dependent events. You will
have to recall the formulas for conditional probability.
P(A∩B) = P(A) ∙ P(B) for independent events A, B.
P(A∩B) = P(A) ∙ P(B|A) for dependent events A, B.
The third Activity #2 involves two readings taken from medical journals. You have to briefly
analyze the conclusions drawn from these studies.
The second Activity #3 is an experiment that explores what happens to chance during
independent and dependent trials. A small prize will be given to the person with the closest guess.
At the end of the lab you will have to hand in the completed lab.
Check all your calculations, sign below and hand in. Thanks.
SIGNATURE: ________________________________________
Activity #1: A Study in Diagnostic Testing
You will be given 10 minutes to complete this activity. Work on this activity with at least one other
student.
A female student is interested in determining whether or not she should PANIC about the positive result
she received when performing a home pregnancy test. To answer her question, she finds the following data
on the accuracy of the pregnancy test she used when performed on 1,000 college-aged women.
Test
Result
True Status
Pregnant (+)
Not Pregnant (-)
Total
Pregnant (+)
48
2
50
Not Pregnant (-)
38
912
950
Total
86
914
1000
1. What percentage of the women in the sample of 1,000 women were pregnant?
2. What percentage of the women in the sample of 1,000 women tested positive?
3. Given a woman is pregnant, what is the probability that she gets a positive pregnancy test?
4. Given a women receives a positive pregnancy test, what is the probability that she is truly pregnant?
5. Based on your above answers, argue one way or the other as to whether the student should or should not panic?
Can you recommend the next step she should take?
Activity #2: Relative measures in Risk Management
You will be given 15 minutes to complete this activity. Read the following two news articles, and then
answer the questions that follow on the back.
Article A --- Plaque Breaks and Heart Attacks
ORLANDO, Fla., Nov. 10 (Reuters)-Researchers say they have found out why sudden
strenuous exercise can bring on a heart attack in
men with blocked arteries.
The fatty plaque that blocks the arteries of
some people with heart disease is delicate and
liable to rupture, they said. Bits of plaque then
block the arteries leading to the heart, causing
heart attacks, the researchers said on Sunday at
the meeting here of the American Heart
Association.
So men with high cholesterol and other
evidence of heart disease who do not exercise
regularly should be careful
about strenuous activity. Dr. Renu
Virmani of the Armed Forces
Institute of Pathology in Washington
and her colleagues studied 146
sedentary men, most of them in their
50's, with heart disease.
The researchers found that those
who died during exercise were more
than three times as likely to have
evidence of ruptured plaque than
men who died during normal daily
activities or while resting.
The plaque burst in 68 percent of
the men who died while engaged in
strenuous activity, compared with 21
percent of the men who died during
normal daily activities.
Dr. Virmani said the men who were doing
exercise, like mowing the lawn, doing
heavy lifting, playing basketball or having
sex, had more vulnerable plaque.
Men who have coronary heart disease and
high cholesterol should be careful about
undertaking vigorous physical activity, and
they should try to lower their cholesterol
through diet or drugs before beginning any
type of exercise program, Dr. Virmani said.
(New York Times, 11/11/97)
Article B --- Being Thin While Pregnant is Seen as Best
By the Associated Press
Women who are very thin
when they become pregnant
for the first time are far more
likely to have healthy babies
than obese women or even
those of normal weight, a
Swedish study has found.
The study, being published
today in the New England
Journal of Medicine,
contradicts the common belief
that heavier women are more
likely to have healthy, fullterm babies.
Although the thinnest women are more likely to have
underweight babies, they are no more likely to give birth
prematurely or to have their babies die in the first week
after birth, the study found.
"Advising lean women to gain weight before
becoming pregnant may not be justified," the researchers
concluded in the study, led by Dr. Sven Cnattingius of
the Karolinska Institute in Stockholm.
The study looked at the medical records of 167,750
Swedish women who gave birth in 1992 and 1993. The
women were divided into four groups based on their
body-mass index: lean, normal, overweight, or obese.
For a woman who is 5 feet 5 inches, for example, a
weight of less than 120 pounds is lean; a weight of 120
to 149 pounds is normal; a weight of 150 to 179 pounds
is overweight, and a weight greater than 180 pounds is
obese.
The researchers then looked for problems: stillbirths
after 28 weeks of pregnancy, infant deaths in the first
week after birth, premature deliveries and low birth
weight.
The mother's weight before pregnancy proved most
important in women having their first babies.
Among first-time mothers, the study found, normal
women had twice the risk of stillbirths compared with
lean women; overweight women had three times the
risk, and obese women had four times the risk. Among
women who already had children, only the most
overweight women had a greater risk of stillbirths than
the thinnest.
The babies of normal, overweight and obese firsttime mothers were twice as likely to die in the first
week of life as the babies of lean women.
(New York Times, 1/15/98)
1.
2.
In article A, what allows the researchers to claim that "those who died during exercise were more
than three times as likely to have evidence of ruptured plaque than men who died during normal
activities or while resting."?
In article B, the journalist reported "the babies of normal, overweight and obese first-time mothers
were twice as likely to die in the first week of life as babies of lean women." Related to this
statement, what isn't reported in Article B that was reported in Article A? Does it matter whether
"this" is not reported?
Activity #3: Your chances in Dependent and Independent Trials
Prologue
There are many situations in which researchers and ordinary people want to know if a certain event will occur. For example, an environmentalist wants to know if
the probability that the water in a well is polluted, a quality control manager wants to know the probability of producing a defective item during a continuous
production process, or a pollster wants to know the probability that voters favor a certain ballot issue. Since we cannot test all wells, check all products, and poll all
voters, we use experiments to estimate probabilities.
Objective
What is the probability that a tossed thumb tack lands with point down?
To answer this question we will perform the experiment in two different ways and find the probabilities.
Question 1: Guess the probability (two decimals) of landing point down if trials are independent? ____________
Question 2: Guess the probability (two decimals) of landing point down if trials are dependent? ____________
1.
Collect Data for independent trails:
(a). Put a single thumb tack in the cup and toss it 30 times and record the number of times it points down.
(b). Copy the values from the other 6 groups. You should now have 210 total tosses.
(c). Fill the last row to determine the relative frequency probabilities.
# of tosses (independent)
30
60
90
120
150
180
210
# landing point down
Relative frequency probability
2.
Collect Data for dependent trails:
(a). Put a 10 thumb tacks in the cup and toss it 3 times and record the number of times it points down.
(b). Copy the values from the other 6 groups. You should now have 210 total tosses.
(c). Fill the last row to determine the relative frequency probabilities.
# of tosses (dependent)
30
60
90
120
150
# landing point down
Relative frequency probability
3.
In your opinion, which of the above experiments gives you a more accurate probability?
180
210