Stumped! Is this probability?

J

JoeyD

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Hi there,

(if this is in the wrong category I apologise)

My head is a little frazzled right now after literally spending all day trying to work this out (I'm terrible at maths I've realised), and I'll try and word this the best I can, but forgive me if it isn't too clear. Help would be incredibly appreciated!

There are 22,632 people.
There are 2854 postboxes.
There are 2,280 letters.
When a letter is posted into one of the 2854 postboxes (randomly, so 1 single postbox could receive 1 or 2 letters with no max), it will always be delivered to any 20 of the 22,632 people.
How many of the 2,280 letters will one of the 22,632 people receive on average after they have all been posted?

Is this even possible to work out? I've literally spent 24 hours on this and I am no clearer! Think I have a mental block so if anybody can help I would be so appreciative,

Thank you in advance.
 
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Just to clarify, when a single letter is posted into one of the 2854 postboxes, 20 people will receive a copy of that 1 letter.
 
I take it this doesn't come from a class on probability; can you tell us what the context is? (We ask for information like this in the summary here.) One reason for that is that people often leave out information in a problem that they don't think is relevant, but it makes all the difference in the world. And the initial goal in problem solving is to make sure we know exactly what we are trying to solve.

My first question is, is each postbox connected to a specific 20 recipients, so that each letter sent to it will go to the same people? Or does it just send them randomly? In the latter case, I don't see that the postboxes have any bearing on the problem; you might as well just say that you send each of the 2280 letters to 20 random people. Am I right?

The second question is, do you know anything about the binomial distribution?

The third question, perhaps even more important, is, what do you mean by "on average"? The answer may be extremely simple, depending on this.
 
Hi, many thanks for taking the time to reply.

I probably should have worded it as it is, rather than try and simplify it, which may have made it more confusing.

1.) Basically each postbox is a contact form on a website, and every time that contact form is filled out (2280 times) it will be received by 20 of the 22,632 people. Out of the 20 recipients attached to that form, 8 will be unique (not attached to any other form) and 12 of them will be attached to one other form (possibly two).

2.) I know zilch about binomial distribution I'm afraid!

3.) By 'on average' I'm trying to work out how many times one of the 22,682 people would possibly receive one of the forms, based on the above.

Hope that makes sense. Math doesn't come easy to me as you can probably tell. Incredibly grateful for your help!
 
First, I'll take the question as stated, where the 20 recipients were entirely random, and you want what we normally call an average.

If by "average" you mean the ordinary average called the "arithmetic mean" (that is, add the numbers up and divide by how many), then the sum of the numbers of letters each person gets will be the total number of letters sent, 2280*20 = 45,600. Divide that by the number of people, 22,632, and the average number per person is 2.015.

If you had really wanted to know something else (such as how many would be expected to get more than one, say), that would be a totally different question. (But it wouldn't be an average.)

I'm not sure whether your extra comments under (1) means the 20 recipients are not random. That would change things.

I'm not sure whether your comment under (3) means you want something other than the average number per person, such as a typical maximum.
 
Again, thank you very much. I also arrived at the 2.015 figure a few times over the last 24 hours, but I didn't believe my workings out, and also couldn't understand how I'd arrived at that figure.

The 20 recipients for (1) wouldn't be random, they would be assigned by a geographical radius. And from what I can calculate, 8 of the recipients would only be in one form, and 12 of the recipients would be in at least one other.

I'm guessing that complicates things so much.

Would that affect the 2.015 figure?
 
Now that I think about it, the average wouldn't be affected by nonrandomness, since you would still be distributing the same total number of letters, as I understand it. I don't fully understand the multiple forms part.

What would change is the distribution of the numbers; without looking at any specifics, it's conceivable that some would be more likely to get none, and others would be more likely to get far more than 2. That is, the average is the same whether everyone gets 2, or half get 0 and half get 4, but the effects would be very different.

That would be much harder to figure out.
 
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