ALTA FINAL PAPER QUESTIONS
AND COMPLETE SOLUTIONS SET
2
◉Trial best fits which of the following descriptions? Answer: one
repetition or instance of an experiment
A trial is defined as one repetition or instance of an experiment.
◉Let S be the event that a randomly chosen voter supports the president.
Let W be the event that a randomly chosen voter is a woman. Identify
the answer which expresses the following with correct notation: The
probability that a randomly chosen voter is a woman, given that the
voter supports the president. Answer: P(W|S)
Remember that in general, P(A|B) is read as "The probability of A given
B". Here we are given that the voter supports the president, so the
correct answer is P(W|S).
◉Let C be the event that a randomly chosen cancer patient has received
chemotherapy. Let E be the event that a randomly chosen cancer patient
has received elective surgery. Identify the answer which expresses the
following with correct notation: Of all the cancer patients that have
received chemotherapy, the probability that a randomly chosen cancer
patient has had elective surgery. Answer: P(E|C)
Remember that in general, P(A|B) is read as "The probability of A given
B," or equivalently, as "Of all the times B occurs, the probability that A
,occurs also." So in this case, the phrase "Of all the cancer patients who
have received chemotherapy" can be rephrased to mean "Given that a
cancer patient has received chemotherapy," so the correct answer is
P(E|C).
◉What is a particular result of an experiment? Answer: outcome
An outcome is defined as a particular result of an experiment.
◉A mathematics professor is organizing her classroom into groups for
the final project. Each student will either be working on a graphing (G)
project or writing a paper (P). Also, each student will be working on an
economics (E), finance (F), sociology (S), or criminal justice (C)
problem. The dots in the Venn diagram below show the different
scenarios.
Let A be the event of a student working on a graphing project.
Let B be the event of a student writing a paper.
Move the dots on the Venn diagram to place the dots in the correct event,
A, B,or A AND B. Note that you might not use all of the dots. Answer:
Event A is the event of a student working on a graphing project, so A
should contain all outcomes with a G.
Event B is the event of a student writing a paper, so B should contain all
outcomes with a P.
Event A AND B should therefore contain all outcomes with both a P and
a G; however, none exist.
Notice also that nothing should be outside of the Venn Diagram because
every project is either a graphing project or a paper.
,◉Let G be the event that a randomly chosen employee of a restaurant is
a General Manager. Let S be the event that a randomly chosen employee
of a restaurant works at a seafood restaurant. Identify the answer which
expresses the following with correct notation: Given that the employee
is a General Manager, the probability that a randomly chosen employee
of a restaurant works at a seafood restaurant. Answer: P(S|G)
Remember that in general, P(A|B) is read as "The probability of A given
B". Here we are given that the employee is a General Manager, so the
correct answer is P(S|G).
◉Let R be the event that a randomly chosen person has red hair. Let G
be the event that a randomly chosen person has green eyes. Place the
correct event in each response box below to show:
Given that the person has red hair, the probability that a randomly
chosen person has green eyes. Answer: 1$G$G
2$R$R
Remember that in general, P(A|B) is read as "The probability of A given
B". Here we want to know the probability that a person has green eyes
given that the person has red hair, so the correct answer is P(G|R).
◉Let M be the event that a randomly chosen student passes a math test.
Let S be the event that a randomly chosen student studies every day.
Identify the answer which expresses the following with correct notation:
The probability that a randomly chosen student studies every day, given
that the student passes a math test. Answer: P(S|M)
, Remember that in general, P(A|B) is read as "The probability of A given
B". Here we are given that the student passes a math test, so the correct
answer is P(S|M).
◉Let S be the event that a randomly chosen store is having a sale. Let M
be the event that a randomly chosen store has marked up their prices in
the last six months. Identify the answer which expresses the following
with correct notation: Given that the store is having a sale, the
probability that a randomly chosen store has marked up their prices in
the last six months. Answer: P(M|S)
Remember that in general, P(A|B) is read as "The probability of A given
B". Here we are given that the store is having a sale, so the correct
answer is P(M|S).
◉Let B be the event that a randomly chosen person has low blood
pressure. Let E be the event that a randomly chosen person exercises
regularly. Identify the answer which expresses the following with correct
notation: The probability that a randomly chosen person exercises
regularly, given that the person has low blood pressure. Answer: P(E|B)
Remember that in general, P(A|B) is read as "The probability of A given
B". Here we are given that the person has low blood pressure, so the
correct answer is P(E|B).
◉A fair spinner contains the numbers 1, 2, 3, 4, and 5. For an
experiment, the spinner will be spun 5 times. If Event A = the spinner
lands on numbers all less than 3, what is an outcome of Event A?
Answer: spinner lands on 1, 2, 1, 2, 2
AND COMPLETE SOLUTIONS SET
2
◉Trial best fits which of the following descriptions? Answer: one
repetition or instance of an experiment
A trial is defined as one repetition or instance of an experiment.
◉Let S be the event that a randomly chosen voter supports the president.
Let W be the event that a randomly chosen voter is a woman. Identify
the answer which expresses the following with correct notation: The
probability that a randomly chosen voter is a woman, given that the
voter supports the president. Answer: P(W|S)
Remember that in general, P(A|B) is read as "The probability of A given
B". Here we are given that the voter supports the president, so the
correct answer is P(W|S).
◉Let C be the event that a randomly chosen cancer patient has received
chemotherapy. Let E be the event that a randomly chosen cancer patient
has received elective surgery. Identify the answer which expresses the
following with correct notation: Of all the cancer patients that have
received chemotherapy, the probability that a randomly chosen cancer
patient has had elective surgery. Answer: P(E|C)
Remember that in general, P(A|B) is read as "The probability of A given
B," or equivalently, as "Of all the times B occurs, the probability that A
,occurs also." So in this case, the phrase "Of all the cancer patients who
have received chemotherapy" can be rephrased to mean "Given that a
cancer patient has received chemotherapy," so the correct answer is
P(E|C).
◉What is a particular result of an experiment? Answer: outcome
An outcome is defined as a particular result of an experiment.
◉A mathematics professor is organizing her classroom into groups for
the final project. Each student will either be working on a graphing (G)
project or writing a paper (P). Also, each student will be working on an
economics (E), finance (F), sociology (S), or criminal justice (C)
problem. The dots in the Venn diagram below show the different
scenarios.
Let A be the event of a student working on a graphing project.
Let B be the event of a student writing a paper.
Move the dots on the Venn diagram to place the dots in the correct event,
A, B,or A AND B. Note that you might not use all of the dots. Answer:
Event A is the event of a student working on a graphing project, so A
should contain all outcomes with a G.
Event B is the event of a student writing a paper, so B should contain all
outcomes with a P.
Event A AND B should therefore contain all outcomes with both a P and
a G; however, none exist.
Notice also that nothing should be outside of the Venn Diagram because
every project is either a graphing project or a paper.
,◉Let G be the event that a randomly chosen employee of a restaurant is
a General Manager. Let S be the event that a randomly chosen employee
of a restaurant works at a seafood restaurant. Identify the answer which
expresses the following with correct notation: Given that the employee
is a General Manager, the probability that a randomly chosen employee
of a restaurant works at a seafood restaurant. Answer: P(S|G)
Remember that in general, P(A|B) is read as "The probability of A given
B". Here we are given that the employee is a General Manager, so the
correct answer is P(S|G).
◉Let R be the event that a randomly chosen person has red hair. Let G
be the event that a randomly chosen person has green eyes. Place the
correct event in each response box below to show:
Given that the person has red hair, the probability that a randomly
chosen person has green eyes. Answer: 1$G$G
2$R$R
Remember that in general, P(A|B) is read as "The probability of A given
B". Here we want to know the probability that a person has green eyes
given that the person has red hair, so the correct answer is P(G|R).
◉Let M be the event that a randomly chosen student passes a math test.
Let S be the event that a randomly chosen student studies every day.
Identify the answer which expresses the following with correct notation:
The probability that a randomly chosen student studies every day, given
that the student passes a math test. Answer: P(S|M)
, Remember that in general, P(A|B) is read as "The probability of A given
B". Here we are given that the student passes a math test, so the correct
answer is P(S|M).
◉Let S be the event that a randomly chosen store is having a sale. Let M
be the event that a randomly chosen store has marked up their prices in
the last six months. Identify the answer which expresses the following
with correct notation: Given that the store is having a sale, the
probability that a randomly chosen store has marked up their prices in
the last six months. Answer: P(M|S)
Remember that in general, P(A|B) is read as "The probability of A given
B". Here we are given that the store is having a sale, so the correct
answer is P(M|S).
◉Let B be the event that a randomly chosen person has low blood
pressure. Let E be the event that a randomly chosen person exercises
regularly. Identify the answer which expresses the following with correct
notation: The probability that a randomly chosen person exercises
regularly, given that the person has low blood pressure. Answer: P(E|B)
Remember that in general, P(A|B) is read as "The probability of A given
B". Here we are given that the person has low blood pressure, so the
correct answer is P(E|B).
◉A fair spinner contains the numbers 1, 2, 3, 4, and 5. For an
experiment, the spinner will be spun 5 times. If Event A = the spinner
lands on numbers all less than 3, what is an outcome of Event A?
Answer: spinner lands on 1, 2, 1, 2, 2
