 # Auuggggh, kid's homework problem! Help!

I’m trying to help my kid with his homework. I thought I was good at statistics, but it turns out I am not. Or at least, I can’t figure out the right numbers to use in the formulas. Can someone spot check at least my initial logic? I feel the question is worded in a very weird way.

I want to say that there are 84 E jobs, 16 L jobs, and 14 (rounded) P+L jobs. Is that correct?

Original question:

84% of a contractors jobs involves electrical work. 75% of a contractors jobs involve plumbing work. Of the jobs that involve plumbing, 90% of the jobs also involves electrical work.
Let E = jobs involving electrical work
L = jobs involving plumbing work
Suppose one of the contractors jobs is randomly selected.
Using the sixth Excel worksheet,
a) Find P(E).
b) Find P(L).
c) In words, what is P(E | L).
d) Find P(E | L).
e) Find P(E and L).
f) Are E and L independent events? Why or why not?
g) Find P(E or L).
h) Are E and L mutually exclusive? Why or why not?

Assuming 100 jobs 84% being electrical would be 84 jobs.

But 14 plumbing jobs would not be 75% of the 100 jobs; it would be 14%.

Your recitation of this problem appears to provide insufficient data. I would argue that not having access to the data on the sixth Excel worksheet puts us at a disadvantage.

He’s in tenth grade, accelerated program. Weirdly, my 7th grade daughter was doing probability earlier this year as well. But hers weren’t this complicated. I don’t remember probability until college. I’m not particularly a math person, although things with proofs tend to be better for me. I argue for a living, and I’d love to argue how this is some exceptional bullshit.

The Excel spreadsheet contains no additional info. It’s just a layout of columns for question, formula used, and answer. It’s a format for submitting answers in a consistent readable way for teacher, not further info.

I went for 84 jobs as E, with the remaining being 16. The 14 represents 75% of that 16 (rounded).

IT’S WORDED SO FUCKING BADLY. C and D seem to be the exact same thing.

Also, never having taken a statistics class, I don’t know how to parse the terms P(E | L), P(E and L), and P(E or L).

But, in an effort to only come out with whole numbers of jobs, I had to assume a minimum of 200 jobs, of which 168 would involve electrical work, 150 would involve plumbing, 135 would involve both. 65 would involve only one trade; 15 would be exclusively plumbing, and 50 would be exclusively electrical.

c) and d) ARE the same thing, but c) is to be expressed in words, and d) is to be expressed (near as I can make out) as a number.

Some people, myself among them, find working with percentages confusing. So it may help to convert percentages to plain numbers. Pick a convenient number of total jobs, say 1000. So you are given that

1. 840 jobs involve electric work (with or without pluming)
2. 750 jobs involve pluming work (with or without electric)
3. You are also given that 90% of the 750 plumbing jobs (0.90*750=675 jobs) involve both plumbing and electric

Now it is a simple matter of subtraction to find

1. the number of electric jobs that don’t involve plumbing
2. the number of plumbing jobs that don’t involve electric
3. the number of jobs that involve neither plumbing nor electric (hint: it’s not zero)

And the percentages asked for can easily be found by division, recalling that we set the total number of jobs at 1000.
Question © and (d) are not asking the same thing. Question © is asking you to put into plain English the meaning of the mathematical expression P(E | L). Question (d) is asking for the numerical value you calculate that P(E | L) has.

Oops. Change those “14s” to “16s.” :smack:

And 75% of 16 is 12, not 14.

Ahhh. I had not considered the possibility that any jobs would involve neither of the trades.

Then in my 200-jobs example, 33 are exclusively electrical and 17 involve neither.

SO far, I have:
a) 0.84
b) 0.16
c) what is the probability of electric job, given plumbing job?
d) 0.14
e) 1.0
f) No, they are overlapping sets but not contingent upon each other
g) ?
h) No, they are overlapping, you horrid sadist. You can definitely have E and L simultaneously, and in fact you do, a significant percent of the time. Knock it off, write some reasonable problems.

Probably should keep that on inside voice…

It SAYS right in the introduction that 75% of the jobs have plumbing. So b) has to be 0.75.

75% of the the subset of jobs. So of the 16 remaining, 75% of those.

a) P(E) is the probability of a job involving electrical work. This is 84%.
b) P(L) is the probability of a job involving plumbing work. This is 75%.
c) P(E | L) denotes the probability of a job involving electrical work if it involves plumbing work…
d) …which is given as 90%.
e) There is a rule of probability that says that P(E and L) = P(L)*P(E | L). Thus, this is .75 * .90 = .675, or 67.5%.
f) If E and L were independent, P(E | L) would be equal to P(E). That is, whether or not a job involves plumbing would make no difference to the probability of it involving electrical work.
g) By another rule of probability, P(E or L) = P(E) + P(L) - P(E and L). Using the numbers above, this is .84 + .75 – .675 = .915, or 91.5%.
h) If E and L were mutually exclusive, that would mean there’s no overlap. No job would involve both electrical and plumbing, and P(E and L) would be 0.

This is all a straightforward application of some basic rules of probability, that your son should have learned about if he’s being given homework like this.

All of this.

For a simple problem like this it would probably be instructive to draw a Venn diagram of the different possibilities.

Where do you see anything about a subset?

Where you seem to have gone wrong is right in the first line, with the ‘84 and 16’ … which looks like you’ve said ‘84 out of a hundred jobs are electrical, so the other 16 out of a hundred have to be plumbing’. Which is not what the question says! All the rest of the tangle you’ve gotten yourself into probably flows from that.

You’re a contractor. You go out on a job, which may require different kinds of work:Plumbing, electrical, carpentry, masonry, demo, painting, etc.