ST 201 Golden West College Basic Probability Venn Diagrams & Conditional Probability Questions question set like previous one, around 3 hours time. Due bef

ST 201 Golden West College Basic Probability Venn Diagrams & Conditional Probability Questions question set like previous one, around 3 hours time. Due before 12:00 califonia time ST 201 – Activity 3
Your name:
Topics:
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Basic Probability
Venn Diagrams
Conditional Probability
Lessons Covered 13-15
Grading:
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Points are listed next to each question and should total 40 points overall.
Late assignments will not be graded. Lowest activity grade will be dropped.
Deadlines:
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Activity Submission: Monday Start of Week 4 – Returned with feedback by following
Saturday.
Activity Reflection and Solutions Discussion Board: Friday End of Week 4
Instructions:
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Download this .docx file.
Type your name in the “Your name:” spot at the top of this document.
Type your answers in this document! We will be grading assignments using Gradescope,
so it is important that your assignment follows the appropriate template.
Insert diagrams or plots as a picture in an appropriate location.
Math Formulas can be included by choosing Insert → Equation.
o Through your enrollment at OSU, you should have access to Word on your
desktop. If for some reason, you cannot use the desktop version of Word, you
can use word via OneDrive (a cloud based version of Microsoft Office); however,
you may not have access to all of the equation features. Do your best to make it
clear what mathematical symbols you are using.
Submit assignment in Gradescope.
Part I. (14 points)
The student information survey data represents 86 students from our class. Among all 86 students
surveyed:
• 35 students say they prefer math over writing
• 66 students reported that the United States is their home country
• 24 students say they prefer math and consider the United States their home country
a) (2 points) If we choose a student at random, what is the chance they prefer math over writing?
P(prefer math) =
b) (2 points) If we choose a student at random, what is the chance they consider the US their home
country?
P(US is home country) =
c) (2 points) If we choose a student at random, what is the chance they prefer math and consider the
US their home country?
P(prefer math AND US is home country) =
d) (8 points) Using the information above, enter the correct proportions for each section of the Venn
Diagram. If it is more convenient for you, write your work on a piece of paper, take a picture of it
and paste it into your document.
iv.
Prefer Math
iii.
i.
ii.
US is home country
Part II. (6 points)
The student information survey data represents 86 students from our class. Among all 86 students
surveyed:
• 35 students say they prefer math over writing
• 66 students reported that the United States is their home country
• 24 students say they prefer math and consider the United States their home country
Please show your work.
a) (2 points) Given a student that considers the US their home country is selected, what is the chance
they prefer math?
P(prefer math | US is home country) =
b) (2 points) Given a student that prefers math is chosen, what is the probability they consider the US
their home country?
P(US is home country | prefer math) =
c) (2 point) Among students in our class, is the event “prefer math” independent from “US is home
country”? Explain. Show mathematical reasoning.
Part III. (14 points)
In the student information survey, you were each asked the following question: Which area of study is
major focused (pick only one)? The table below shows the distribution of answers to this question.
Major
Business
Count
Probability
19
Engineering
2
Liberal
Arts
2
Psychology
Science
15
37
Social
Sciences
10
Education
1
a) (7 points) Fill in the probability of randomly selecting a student from each of the majors. Round to 3
decimal places.
b) (3 points) Check your probability model. Explain reasoning or show work for each check.
✓ Are the evens assumed to be disjoint/mutually exclusive?
✓ Is each probability between 0 and 1?
✓ Do all the probabilities add to 1? (Is okay if it is just slightly off due to rounding)
c) (2 points) If we choose one student at random, which major is the most likely to be selected?
d) (2 points) What is the chance you select a student with a major in either Business or Psychology?
P(Business or Psychology) =
Part IV. (6 points)
In a bookstore, the probability a customer buys a novel is 0.55 and the probability that the customer
buys a non-fiction book is 0.35. Suppose the probability that the customer buys both a novel and a nonfiction book is 0.2.
a) (2 points) Find the probability that the customer buys either a novel or a non-fiction book.
b) (2 points) What is the probability that a customer doesn’t buy a book or a novel?
c) (2 points) Find the probability that a customer buys a novel given they are purchasing a non-fiction
book.

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