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I have a simple scenario as follows:

If 12% of people buy a new computer each year, 33% of people buy shoes each year, and 39% of people buy a new phone each year, what percentage of people on average buy at least one of those products each year?

Is there a specific answer? I can see that the answer might be a range, but is there a way to express with maybe a specific value and a standard deviation?

Im sure its a reasonably simple answer but my memory for maths is not great it turns out. Any help appreciated!

Thanks!

EDIT:

I've actually run a quick simulation in code on this and the results are pretty consistently ~64 out of a sample of 100 people buy at least 1 product. Surely there is a mathematical proof for this though?

SR.
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  • Is this all the information you have? I may be missing something but I feel using a Venn diagram to represent this problem is appropriate, however I'm not sure there is enough data to solve it. – Loocid Sep 22 '14 at 02:28
  • @Loocid yep thats all the info. I guess a venn diagram could help but im really after any techniques that could be used to determine a reasonably specific figure.

    Im kind of working on the angle of trying to apportion maybe 1/3 of each group to the other groups and do a calculation that way but not even sure how to do that really as its been a long time since ive needed maths!

     – SR. Sep 23 '14 at 05:05

1 Answers1

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If everybody who buys a computer buys shoes and everybody who buys shoes buys a new phone, then $39\%$ of people buy at least one item. If each person buys exactly one of the three items, then $84\% = 12\% + 33\% + 39\%$ buy at least one of the items. To get a more precise answer, we would need to know what percentage of people buy each pair of items and what percentage of people buy all three items.

N. F. Taussig
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  • Thanks N.F.!

    I guess thats the tricky thing; we don't know how many people buy each item.

    So i guess im kind of looking for a way to say if the shoe computer buyers buy an average amount of shoes and phones (and same for the other groups), can we work out any sort of average of how many people buy an item?

    Even a rough number or range?

     – SR. Sep 22 '14 at 03:33