Stats/Maths Question

oldbag · 24 Apr 2013 at 17:59

Saw this on the train as part of an advert for "Dara O'Briains school of hard sums".

With the risk of looking an idiot. Is the answer to the following dead obvious?

If 70% of people on this train had beans this morning, 75% had eggs, 80% had sausages and 85% had toast, how many definitely had a full English breakfast?
And did any of them have beans down their shirt?

I thought the answer was 22.5 but that's probably completely wrong!

valkynaz · 24 Apr 2013 at 18:10

0%. Where's the bacon?

|Thomas| · 24 Apr 2013 at 18:10

None.

We don't know about bacon, tomatoes, hash browns etc

Dis86 · 24 Apr 2013 at 18:15

How many were on the train?

Disco Boy · 24 Apr 2013 at 18:21

If the chance of having each item is independent, then...

.7*.75*.8*.85= .357 = 35.7%

Gives a probability, but not a certainty.

Where did you get 22.5 from?

oldbag · 24 Apr 2013 at 18:24

30 + 25 + 20 + 15 / 4

Or I thought 100 - the above additions and forget the division by 4.

Disco Boy · 24 Apr 2013 at 18:27

oldbag said:
30 + 25 + 20 + 15 / 4

Or I thought 100 - the above additions and forget the division by 4.

Okay, well I'm not sure where you got that crom. Here was my logic.

If the probability of A happening is x and the probability of B happening is y. Then the probability of both A and B happening is x*y.

Zenith · 24 Apr 2013 at 18:34

I reckon 10%, but I also agree that's it's not a full English without bacon.

muon · 24 Apr 2013 at 18:36

how many definitely had a full English breakfast?

Need to take this into mind when answering. You don't just multiply probabilities together.

Need to use basic set theory or conditional probabilities. Either will give the correct answer.

isonomicjedi · 24 Apr 2013 at 18:36

Nobody had an English breakfast as most of the stuff was imported.

Elixir · 24 Apr 2013 at 18:39

How many DEFINITELY had it is 10%, if we ignore that not all the ingredients are there.

EDIT: You assume the people who didn't have a certain item are separated as much as possible... so you can add together all the %s of people who didn't have each item, subtract from 100 and that'll give you the % that must have had all of them.

Dolly · 24 Apr 2013 at 18:41

Let N be the number of people. For each person, create 4 "holes" which can potentially receive eggs, bacon, toast or beans. That's 4N holes in total. The total amount of food distributed is

70N/100 + 75N/100 + 80N/100 + 85N/100 = 31N/10

(where obviously N is such that each of these are integers!). So the total number of empty "holes" will be

4N - 31N/10 = 9N/10

To get a lower bound on the number of people with full english (i.e. people with all four holes full), we should give only one of the 9N/10 to any player. There will always be N/10 players who can't receive a "hole". So the lower bound is N/10, or 10%.

oldbag · 24 Apr 2013 at 18:46

So basically 100 - 90 = 10 (90 is the total of 30 + 25 + 20 + 15)

muon · 24 Apr 2013 at 18:46

Elixir said:
How many DEFINITELY had it is 10%, if we ignore that not all the ingredients are there.

EDIT: You assume the people who didn't have a certain item are separated as much as possible... so you can add together all the %s of people who didn't have each item, subtract from 100 and that'll give you the % that must have had all of them.

Yep at least 10% definitely had it though.

10% isn't necessarily how many had it.

Elixir · 24 Apr 2013 at 18:47

muon said:
Yep at least 10% definitely had it though.

10% isn't necessarily how many had it.

The word definitely is in the question.

oldbag said:
So basically 100 - 90 = 10 (90 is the total of 30 + 25 + 20 + 15)

Yup.

isonomicjedi · 24 Apr 2013 at 18:47

I don't know about the maths but suggest they try muesli.

muon · 24 Apr 2013 at 18:49

Elixir said:
The word definitely is in the question.

You don't know for definite how many had it.

As Dolly said, you have a lower bound in the set of outcomes.

Elixir · 24 Apr 2013 at 18:50

muon said:
You don't know for definite how many had it.

As Dolly said, you have a lower bound.

You know that 10% definitely had it. It's possible, with other distributions of who had what, that up to 70% of people could have had it. But the question is how many definitely had it, and the answer to that is 10%.

oldbag · 24 Apr 2013 at 18:50

Cheers peeps.

muon · 24 Apr 2013 at 18:52

Elixir said:
You know that 10% definitely had it. It's possible, with other distributions of who had what, that up to 70% of people could have had it. But the question is how many definitely had it, and the answer to that is 10%.

When I was at university, such sloppy language will lose you marks.

At least 10% definitely had all ingredients.

Not 10% definitely had all ingredients.

edit:

of course wouldn't be answering in words which would help things.