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There are two brand shops - A and B. A manufactures 1000 laptops, of which 100 are defective. B manufactures 100 laptops, of which 10 are defective. When I go to buy at a shop of any brand, they simply pick a laptop at random and give it to me. Which shop should I buy from - A or B?

I was given this problem by a friend who's into tricky puzzles, so I'm skeptical that this will be straightforward. I'm thinking that in both cases there's a 10% chance of getting a defective laptop. So I guess both shops are equally fine to buy from? Am I missing something here and is there a more involved solution to this?

user9343456
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1 Answers1

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Buying from either has a $\frac{1}{10}$ chance of yielding a broken laptop, you are not missing anything. Buying from A and B is therefore equally good if we are to consider the purchase as a single occurrence.

However, I would wit that one should buy from store B. Suppose the first laptop is defective and one returns it to the store to be replaced by another random laptop: in store B one has a $\frac{90}{99} = \frac{10}{11}$ chance of getting a working replacement, while store A would only give a $\frac{900}{999} = \frac{100}{111}$ chance.

kviiri
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  • +1 Considering chances of a successful replacing a defective laptop extends a problem past the original scope. Anyway, it is a very interesting extension, which shows how the solution discussion may look like. Thank you. – CiaPan Jun 10 '22 at 08:20
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    @CiaPan As the friend who posed this question likes tricky ones, I figure the intended solution might contain a twist like that ;) – kviiri Jun 10 '22 at 08:26
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    @CiaPan: I would buy from store A, because if all the ordinary people uses kviiri's reasoning and buys from store B, it would run out of working laptops faster than A would. So I am more likely to be able to replace a defective laptop if I buy from A. – user21820 Jun 10 '22 at 16:09