Average of percentages

Question

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?

Answer 1

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.