Statistical Problem dealning with Probability

[Withoutlogic]

Hi all, I'm an English major in an introductory statistics class that is required for my gen ed curriculum. Quite simply, there is a reason why I am not majoring in anything to do with numbers as I am awful at all of it. I have this probabilities problem that I have been staring at for an hour and I have no idea how to get started.

Homework Statement

37% of accountants purchased their computer hardware by mail order direct and that 54% purchase their computer software by mail order direct. Suppose that 97% of the accountants who purchase their computer hardware by mail order direct purchase their computer software by mail order direct. If an accountant is randomly selected determine the following probabilities:

a. The accountant does not purchase his computer software by mail order direct given that he does not purchase his computer hardware by mail order direct.

b. The accountant does purchase his computer software by mail order direct given that he does not purchase his computer hardware by mail order direct.

c. The accountant does not purchase his computer hardware by mail order direct if it is known that he does purchase his computer software by mail order direct.

d. The accountant does not purchase his computer hardware by mail order direct if it is known that he does not purchase his computer software by mail order direct.

Homework Equations

(P)A|B = A intersect B/(P)B
(P)B|A = A intersect B/(P)A

The Attempt at a Solution

I don't understand what parts of the problem I have to use in order to get the correct answer. My brain wasn't made to think this way. I am lost and going to this board is pretty much a final option. I am in desperate need of some short term help.

Is part a solved by .03/.37? This is as far as I have gotten.

 

[haruspex]

Suppose that 975 of the accountants who purchase their computer hardware by mail order direct purchase their computer software by mail order direct.

Should that be 97%?

 

[Withoutlogic]

Yes, it should. I'm sorry. Very stressed out right now. The main thing that has thrown me off is the "Suppose that 97% of the accountants who purchase their computer hardware by mail order direct purchase their computer software by mail order direct". If you multiply 37% by 3% you end up with 1.11%. If you subtract that from 37% you end up with 35.89%. Is this the percentage of accountants who purchased both (the intersection) from mail order direct?

 

[haruspex]

"Suppose that 97% of the accountants who purchase their computer hardware by mail order direct purchase their computer software by mail order direct". If you multiply 37% by 3% you end up with 1.11%. If you subtract that from 37% you end up with 35.89%. Is this the percentage of accountants who purchased both (the intersection) from mail order direct?

Yes. Given that you are struggling with this, I'm going to suggest that, at this stage, you don't worry about the equations but just apply simple logic.
Can you write out the percentages of all four combinations. Call these HmSm, HmSo, HoSm, HoSo for "hardware-mail-software-mail" etc. Which two combinations are of interest in answering a)?

 

[Withoutlogic]

I have no idea. I am going to fail this class and not be able to graduate because of it. I got through Calc with a B but this has defeated me.

 

[haruspex]

I have no idea. I am going to fail this class and not be able to graduate because of it. I got through Calc with a B but this has defeated me.

Don't despair!
You already have HmSm = 35.89%, HmSo=1.11%. And you know that HmSm+HoSm=54%. So what is HoSm? And you know the sum of all four is 100%, so you can also deduce HoSo.

Part b) says: "given that he does not purchase his computer hardware by mail order direct." So this accountant is known to be in one of two combinations. Which two?

 

[Withoutlogic]

HoSm would be 18.11%, and HoSo is 35.89.

So B would be HmSm at 18.11% given Ho which would be 63%? Which would be .1811/.63?

I really, really am appreciating the help Sir or Ma'am.

 

[haruspex]

HoSm would be 18.11%, and HoSo is 35.89.

So B would be HmSm at 18.11% given Ho which would be 63%? Which would be .1811/.63?

You meant HoSm, not HmSm, but your numbers are right. Well done.

 

[Ray Vickson]

Hi all, I'm an English major in an introductory statistics class that is required for my gen ed curriculum. Quite simply, there is a reason why I am not majoring in anything to do with numbers as I am awful at all of it. I have this probabilities problem that I have been staring at for an hour and I have no idea how to get started.

Homework Statement

37% of accountants purchased their computer hardware by mail order direct and that 54% purchase their computer software by mail order direct. Suppose that 97% of the accountants who purchase their computer hardware by mail order direct purchase their computer software by mail order direct. If an accountant is randomly selected determine the following probabilities:

a. The accountant does not purchase his computer software by mail order direct given that he does not purchase his computer hardware by mail order direct.

b. The accountant does purchase his computer software by mail order direct given that he does not purchase his computer hardware by mail order direct.

c. The accountant does not purchase his computer hardware by mail order direct if it is known that he does purchase his computer software by mail order direct.

d. The accountant does not purchase his computer hardware by mail order direct if it is known that he does not purchase his computer software by mail order direct.

Homework Equations

(P)A|B = A intersect B/(P)B
(P)B|A = A intersect B/(P)A

The Attempt at a Solution

I don't understand what parts of the problem I have to use in order to get the correct answer. My brain wasn't made to think this way. I am lost and going to this board is pretty much a final option. I am in desperate need of some short term help.

Is part a solved by .03/.37? This is as far as I have gotten.

A way that is often useful for people who are having trouble understanding/calculating in such problems is to just use simple numbers and elementary arithmetic. This helps to put the *logic* in perspective.

So, suppose we look at 1,000,000 accountants. How many of them purchased hardware by mail order (MO)? How many of them purchased software by MO? How many did not purchase hardware by MO, and how many did not purchase software by MO?

You are told that 97% of the hardware MOs also purchased software by MO. So, how many accountants is that? Knowing that figure, you can compute how many hardware MOs did not do software MO, etc.

Once you have all that, you can get the conditional probability P(not software MO|now hardware MO) just by looking at the ratio Number(not software MO and not hardware MO)/Number(not hardware MO).

To clarify: of the 1,000,000 accountants, a certain sub-population of them do not order hardware by MO. When computing conditional probabilities *given* not hardware MO, we are just looking at the "not hardware MO" sub-population, and are asking for the proportion of that sub-population who order software by MO or not.

Later, when all this becomes familiar, you can streamline and automate it using formulas, but until you are comfortable with the concepts, a more laborious (but more straightforward) approach may be preferable.