I need help trying to better understand question b and c please

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jcooper015

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I provided an attachment
 

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  • Probability_Simple and Joint_Assignment (1).pdf
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Hello, and welcome to FMH! :)

Many of our helpers, myself included, don't want to go to the trouble of having to download and open a pdf file. You'll be much more likely to get prompt help if you post the question such that it can be read here.
 
An investment-newsletter writer wanted to know in which investment areas her subscribers were most interested. A survey was sent to 331 randomly selected professional clients, with the following results:

Business ​
Stocks ​
Bonds ​
CD’s ​
Commodities
Options ​
Total ​
Doctors
30​
25​
15​
2​
0​
72​
Lawyers
29​
34​
12​
0​
5​
80​
Bankers
50​
35​
29​
5​
10​
129​
Others
21​
14​
10​
3​
2​
50​
TOTAL
130​
108​
66​
10​
17​
331​

A. What is the probability that an investment client is a doctor?
B. If an investment client’s main investment interest is stocks, what is the probability that he or she is a banker?
C. What is the probability than an investment client’s main interest is not in bonds?
 
Here is your question:

FMH117568.png

The next thing we need from you is your work! (You did read our submission guidelines, right?)

You want to "better understand" parts b and c; please show us what you currently understand (starting with part a) so we can see what help you need.
 
A. 72/331=.2175 or 21.75%
B. (130/331+129/331)-50/331=not sure
C. 1-(108/331)=.6737 or 67.37%
 
They have given you, in the rightmost column, the clients by occupation. They have also given you, in the bottommost row, the clients by interest. So this "cross-tab" makes it really easy to answer these questions.

You got #a right. You read across the doctor row to find the total number of doctors sampled and divided by the grand total of those sampled in the southeast cell. Good

Now for #b. You are interested in those who selected stocks and are bankers. At the bottom of the second column is the total of those who selected stocks, namely 130. The intersection of the stock column and the banker row show that 50 bankers are interested in stocks. So what do you think the probability requested is?
 
jcooper015 said:
A. 72/331=.2175 or 21.75%
B. (130/331+129/331)-50/331=not sure
C. 1-(108/331)=.6737 or 67.37%
Click to expand...
What you found for B is the probability that a client is interested in stocks or is a banker.

That question is asking for the probability that a client is a banker given that their interest is in stocks. That is, restricting our attention to the stocks column, what is the probability that someone is a banker?
 
jcooper015 said:
B. 50/331=.1510 or 15.10%
Click to expand...
No, that's the probability of being a banker who likes stocks (an "and" question).
jcooper015 said:
Sorry
129/331=.3897 or 38.97
Click to expand...
That's the probability of being a banker, period (like part a).
jcooper015 said:
could B be
(130/331) x (129/331)-50/331=.0020 or 20 %
Click to expand...
That seems to be an "or" assuming wrongly that bankers and stocks are independent.

Take what I said very literally: Cover everything except the Stocks column, and think about the probability that someone in that smaller population is a banker.

Or, quote the definition you were given for conditional probability, and we can start with that to find P(banker | stocks).
 
Can you try to explain in easier terms please! I am not very bright when it comes to this kinda thing. Is there a formula that you can give me so I can figure it out please. Then I can give you an answer to see if I am correct.
 
I'm presuming you were taught a formula; that's why I asked you to state the definition you were given for conditional probability. Can you do that? That's the place to begin.
 
jcooper015 said:
Can you try to explain in easier terms please! I am not very bright when it comes to this kinda thing. Is there a formula that you can give me so I can figure it out please. Then I can give you an answer to see if I am correct.
Click to expand...
Look at the table.

How many are interested in stocks? That is group one.

How many of those in gruop one are bankers? That is group two.

So if you select someone at random from group one, what is the probabilty that person selected also is in group two?

As Dr. P has said, you can get the answer by remembering one of the basic formulas of probability theory, but you can also get the answer from the table and common sense. Doing it the latter way will show you the reason behind the formula.
 
jcooper015 said:
(130+50)/331=.5438
Click to expand...
You need to stop making wild guesses.

What is 130? What is 50? When you add those together, does the resulting sum represent anything?

Answer another question. In all of your guesses, you have divided by 331. WHY?
 
Let's actually do what I suggested:
Dr.Peterson said:
Cover everything except the Stocks column, and think about the probability that someone in that smaller population is a banker.
Click to expand...
Here it is:
FMH117568 conditional.png
Those are all the people interested in stocks. You are asked,

If an investment client’s main investment interest is stocks, what is the probability that he or she is a banker?​

So, among these people (those interested in stocks), what is the probability of being a banker?

This is what conditional probability is.
 
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