Stat 432: Homework 1
1. 44.6% of all undergraduate students at ISU are female. 12.5% of all undergraduate
students at ISU are in the College of Agriculture and Life Sciences (CALS). 5.2% of
all undergraduate students at ISU are females in CALS. An undergraduate student is
selected at random from all undergraduate students at ISU. Find the following
probabilities.
a. The probability that the student selected is a female or in CALS.
b. The probability that the student selected is a male.
c. The probability that the student selected is a male not in CALS.
d. Given that the student selected is in CALS, what is the probability that the student
is female?
e. Given that the student selected is a female, what is the probability that the student
is in CALS.
f. Are selecting a female and selecting a student from CALS independent? Support
your answer by referring to appropriate probabilities.
2. Suppose it is know that 1 out of 1000 people in the general population have a
particular disease. A test for the disease will show a positive result 99% of the time
when given to people with the disease. The test will show a negative result 98% of
the time when given to people without the disease.
a. Just looking at the probabilities that the test correctly identifies whether a patient
has the disease or not (e.g. positive when disease is present and negative when
disease is absent) would you say this test will be useful to doctors in diagnosing
the disease? Explain briefly.
b. If the test turns out to be positive what is the chance the patient has the disease.
c. If the test turns out to be negative what is the chance the patient does not have the
disease.
d. Looking at the probabilities in b and c, would you say this test will be useful to
doctors in diagnosing the disease? Explain briefly.
e. A new research company wants to develop a new test where p = probability the
new test shows a positive result given the patient has the disease and p =
probability the new test shows a negative result given the patient does not have
the disease. What does p have to be in order that the probability the patient has
the disease given the new test turns out to be positive is 0.95?
3. In a best 3 out of 5 championship series two teams play each other at most five times.
The first team to win 3 games wins the championship and no additional games are
played. When Team 1 plays Team 2, Team 1 wins 60% of the time.
a. Construct the sample space of possible outcomes for Team 1 when it plays Team
2 in a best 3 out of 5 championship series.
b. What is the chance that Team 1 wins the championship?
c. Given the championship is decided in three games what is the chance Team 1 won
the championship?
d. Given the championship is decided in five games what is the chance Team 1 won
the championship?
4. P(A or B) = P(A) + P(B) – P(A and B). What does P(A or B or C) equal?