Expert answer:Identifying unconditional and conditional probabil
Solved by verified expert:I have a writeup here that gives some examples of how to recognize whether a statement is conditional or unconditional probability, and how to write it in notation.Look this over first, Identifying unconditional and conditional probabilities-3.docxThen do the following problems to hand inPracticing identification and notation for unconditional and conditional probabilities (1)-1.docxIf you type in your answers, you should upload the file as .doc or .docx.If you hand write your files and take a photo, please import the photo image into either of the above types, or make it a pdf. While Canvas lets you upload jpg files, they are difficult to grade because they are imported at 3 times actual size (visually) of the other types, which look ‘normal’ on the Canvas grading viewer AND that file time doesn’t allow zooming in or out for some reason. That is why I am restricting the file types. If you take a photo, please make sure your work is legible, no shadows on the work, the handwriting is dark enough to be read, etc. Thank you. This exercise is important not just for helping with midterm 2 (and the final), but also for when you need to set up and use Bayes’ Rule in decision analysis in BUS 190. If you can’t tell the difference between P(A|B) and P(B|A) in a word problem, you will likely get those problems wrong. It is also important in real life to recognize ‘conditioning’ statements. You might find them in Marketing Research reports, for example. You will certainly see them in polls, although not necessarily stated directly as a probability.
identifying_unconditional_and_conditional_probabilities_3.docx
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Identifying unconditional and conditional probabilities.
From probability you studied in elementary statistics, you are supposed to remember that probabilities
deal with the relative frequency that an event occurs in a population. The denominator is the count of
the population, and the numerator is the number of times that event occurs in the population.
Population is just a general term. It just means the group we are talking about. That group could be a
population such as the population of the US, or of California, or of San Jose. But it could also be all the
products you sell in a store, or all the mutual funds available, or all the pets you own, or all the days in
the past year. In a probability problem, you first need to identify the population. It will be the biggest
group that the problem is talking about.
For example, I could ask, what is the chance that a student randomly selected from our class is male?
The ‘population’ is our class. We are ignoring the fact that it is a subset of SJSU students, or residents of
California, or of the US, or the world. This chance is the probability that a member of our class is male.
For conditional probabilities, you need to identify the subpopulation that the new probability is about.
That is usually called the ‘conditioning event.’ So there has to be first, a population, then second, a
subpopulation that you are restricting your attention to.
So, I could ask the following questions:
1. What is the chance that a randomly selected student in our class got an ‘A’ in statistics?
2. What is the chance that a randomly selected male student in our class got an ‘A’ in statistics?
3. What is the chance a randomly selected student in our class who got an ‘A’ in statistics is male?
The notation would be:
1. P(student in class got A in statistics) – or even more reduced: P(A)
2. P(student in class got A in statistics|student is male) – or even more reduced: P(A|M)
3. P(student in class is male|student got A in statistics) – or even more reduced: P(M|A)
where A stands for ‘student got an A in statistics’ and M stands for ‘student is male’
In the first case, I am talking about anyone in our class population. But in the second two problems, I am
restricting to the subpopulation of male students in the case of the second question, or a student who
got an A in statistics in the second question.
Sometimes there are marker words that help you distinguish. I mentioned the words ‘given,’ ‘if,’ and
‘when’ as examples in class. For example,
4. Given a student in our class is female, what is the chance she got an A in statistics?
5. If a student does well in the quizzes, what is the chance he or she will do well on the final?
6. What is the chance a student does well on the final when he or she has a full-time job during the
summer session as well?
So notice that I have given key words to highlight the conditioning events. I am still talking about
students in our class, but I am breaking them up into subpopulations for the probabilities.
4. P(A|F)
( where F = female student)
5. P(Well on final|well on quizzes)
6. P(Well on final|has full-time job in summer session)
Sometimes the word ‘of’ can be a clue to the conditioning event or subpopulation, as in the following
examples:
7. What is the chance of a female student having a full-time job in summer session?
8. What is the chance of a student who did all the homework to do well on the final?
9. What is the chance of a student whose native language is not English to do well on the final?
Notation:
7. P(full-time job in summer session | F)
8. P(do well on final|did all homework)
9. P(do well on final|native language not English)
I will set up some more examples for you to practice on.
Practicing identification and notation for unconditional and conditional probabilities
Write the following in proper notation, and tell me what your variables mean if you are not using English
phrases.
You are a marketing researcher and are interested in studying all the customers of all your products.
1. What is the chance that a randomly selected customer is between 18 and 24 years of age?
2. What is the chance of a female customer being between 18 and 24 years of age?
3. What is the chance that a customer who is between 18 and 24 years of age is female?
4. What is the chance that a randomly selected customer makes between $50K and $75K inclusive, per
year?
5. Given a married male customer, what is the chance he makes between $50K and $75K inclusive, per
year?
6. what is the chance a married female customer makes between $50K and $75K inclusive, per year?
You own and run a retail clothing store and want to see what is selling or not. Put the numbers to your
notation as appropriate. Your sales are split 50-50 between men’s and women’s clothing.
1. 25% of your sales are of large size garments.
2. If a sale is of a large-size garment, the chance it is a men’s garment is 60%.
3. If a sale is of a woman’s garment, the chance it is large size is 30%.
4. When a sale is of a pink garment, the chance it is a women’s garment is 90%.
5. If a sale is of a women’s garment, the chance it is pink is 10%.
6. The chance a garment sold is pink is 3%.
…
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