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Original poster

Maths level 5

42 replies

missk167 · 21/10/2021 13:00

Hey everyone am doing my level 5 in maths for my level 5 in social care

I'm at the stage where am going bang my head against a brick wall ahhhh.

I'm stuck on probability I've done research and can only find questions on coins or dice. Can anyone help me work this out please.

Out of 507 people, 248 people work in retail and 172 people are self employed. What is the probability that a person either works retail or is self employed?

I'm tried looking at seminars, practice exam papers and I'm struggling with working this out ahh.

Thank you

OP posts:

Silversilverstreet · 21/10/2021 15:23

The OP needs to do 1 - probability of neither

@TeenMinusTests, how do you work out the probability of neither, though?

In my opinion, if this is all this badly-written question tells you, the only way to answer it is to assume that people only have one job. So, if they work in retail they can’t be self employed as well.

@missk167, are you able to answer merryhouse’s questions posted at 14:00? They are useful stepping stones on the way to answering the more complicated question in your first post.

If you can’t I (or we) need to find you an explanation of probability right from the start. Reading the answers to the questions here might help as a start.

PeppermintMocha · 21/10/2021 15:27

@TeenMinusTests, how do you work out the probability of neither, though? *

Exactly. This is a badly written question, with the implied assumption that people are in only one of those categories. And therefore adding the groups is fine.

You can't work out the probability of neither in any way other than by also making that same assumption.

Given the level of maths that this is for, it is a reasonable assumption to make, although there shouldn't be a need for making assumptions at all.

OP, perhaps change the question to red and orange sweets or something, and try to solve it then.

Silversilverstreet · 21/10/2021 15:29

This starts with a bit of background and tells you more than you need to know to answer this question but will be useful for other probability questions at this level. The method you need is shown in examples on page 3.

TeenMinusTests · 21/10/2021 15:30

p(not retail) = (507-248)/507 (or 1 - 248/507)
p(not self employed) = similar to above

p(neither) = p(not retail) x p(not self employed)

p( retail or self employed or both) = 1 - p(neither)

TeenMinusTests · 21/10/2021 15:33

Or am I having a complete brainstorm?

TeenMinusTests · 21/10/2021 15:37

I would do this with a probability tree diagram.

Silversilverstreet · 21/10/2021 15:45

IGNORE THIS BIT, OP!

@TeenMinusTests,

P(neither A nor B) does not equal p(not A) x p(not B)

Say you have 10 people. 1 works in retail (R) , 3 are self employed (SE)
6 are neither (N)

6 out of 10 are neither. P(N) = 6/10
9 don't work in retail. P(not retail) = 9/10
7 are not self employed. P(not self employed) = 7/10

6/10 does not equal 9/10 x 7/10

I can show this with a Venn diagram but can't draw one in the MN message box.

TeenMinusTests · 21/10/2021 16:06

Silver You are assuming that retail and self employed are mutually exclusive. Which if it said X work in retail and Y work in farming they would be.
However as far as I can see you can work in retail and be self employed, eg running your own shop.

As the OP has worded it, I (obviously) think my interpretation is correct, though I accept I could be wrong and the question could have used different examples for improved clarity.

If it was
507 pupils in a school. 248 have a dog. 172 like spaghetti. What is the probability a child either has a dog or likes spaghetti, you could see these are independent things.

I am interpreting it as independent as that is how I have seen GCSE questions go when similarly worded.

But I do accept the question setter may have assumed differently.

PeppermintMocha · 21/10/2021 16:24

Yes there are questions where there could be overlaps like you are thinking of, but you'd need more information if that were the case. There's not enough info here for that to work, so it can only be solved by assuming they are mutually exclusive categories.

TeenMinusTests · 21/10/2021 16:36

You don't need more info if they are independent.
Though I agree you can argue either way.

Lougle · 21/10/2021 16:43

Out of 507 people, 248 people work in retail and 172 people are self employed. What is the probability that a person either works retail or is self employed?

If this is the entirety of the question, then we have to assume the two groups of people are mutually exclusive.

P (retail) is 248/507; P (self-employed) is 172/507.

'Or' means that you add (and would mean that you multiply).

248/507 + 172/507 = 420/507

I do think you'd benefit from some support, @missk167 to get the basics. But you can do it.

Lougle · 21/10/2021 16:44

In decimal terms P=0.83 (2d.p.)

yodaforpresident · 21/10/2021 16:48

@TeenMinusTests I didn't assume anything - I asked the OP to check, given I hadn't actually seen the problem. Perhaps you could work on your comprehension skills and possibly your people skills too.

Silversilverstreet · 21/10/2021 17:53

@TeenMinusTests, yes, you’re right, I am assuming they are mutually exclusive. That’s what I put in my post to you at 15:23.

GCSE questions do have questions where events aren’t independent. That’s where the tree diagrams you mention are very helpful, and are sometimes drawn as part of the question where you have to fill in the gaps. (Or, used to be. I’ve not seen any new ones since 2014 when my school changed to IGCSE.)

I think this a bit beyond where the OP currently is, though.

TeenMinusTests · 21/10/2021 19:18

yoda I wasn't disputing your first statement.

Silver I agree that tree diagrams seem to be beyond where the OP is right now. The trouble is we aren't seeing this question in context with other work being done, how it is directed etc. Which is why it is hard to gauge the level the question is likely to be at.

Despite the fact that I really am trying to help the OP, the consensus seems to be that people think I'm not, so I'm out.

OP good luck. Please try to get yourself some direct assistance, I think it could really ghelp you reach your goal.

PeppermintMocha · 21/10/2021 19:58

(OP, ignore this bit too!)

*You are assuming that retail and self employed are mutually exclusive. Which if it said X work in retail and Y work in farming they would be.
However as far as I can see you can work in retail and be self employed, eg running your own shop.

As the OP has worded it, I (obviously) think my interpretation is correct, though I accept I could be wrong and the question could have used different examples for improved clarity.

If it was
507 pupils in a school. 248 have a dog. 172 like spaghetti. What is the probability a child either has a dog or likes spaghetti, you could see these are independent things.*

I think what we are saying is that this question would be impossible to answer based on the given information, unless you assume that the two groups are mutually exclusive - which would be a silly assumption given the example of dogs/spaghetti, of course, but there is no other way to solve the problem. Given the actual question, with retail and self-employed, it is much more reasonable to assume they are likely to be mutually exclusive categories, particularly since you couldn't solve the problem any other way.

To use your dogs/spaghetti example - you couldn't know how many of the dog lovers liked spaghetti or vice versa; it could be all of them or none of them. There's no way to work out any probabilities in that case.

If the question had say "the probability of someone liking dogs is 248/540, and the probability of someone liking spaghetti is 172/540, what is the probability that a randomly selected person likes both/neither/one or the other", then that would be solvable - and in that case, yes, using tree diagrams could be helpful. Giving the probabilities of these events, however, is very different than giving the number of people in the groups as is the case here!

So it's impossible to solve it any other way than assuming the categories are mutually exclusive, and given the actual categories and the level that the OP's course is, that would really be the most sensible interpretation, even though it's poorly worded because it is possible that there could be people in both categories. While that would be an interesting question for slightly more advanced GCSE students, you would need further information to draw a Venn diagram or equivalent.
It's also poorly worded by not saying that the person in question is 'randomly selected'!

yodaforpresident · 22/10/2021 15:48

@TeenMinusTests

OP. You really can't just keep coming on to MN with every maths problem you get.

To give you starters.
Both previous posters are incorrect, you can't assume no overlap.

Find out probability of neither retail nor self employed.

Then probability of one or the other or both is the previous number subtracted from 1.

You need to go back to your maths teacher. You are clearly struggling, you need extra help, not just answers from MN

If you need to be able to do maths for your qualification, you need to be able to do it.

@TeenMinusTests given that I was one of the “two previous posters” what were you disputing?

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