Imagine you have two piles of six flares each. One pile includes three useless flares. Call that the bad pile, although you don't at first know which group is bad. To test a flare, you must light it (because they all look good). Once you do that, you'll find out whether it works or not. But even if it is good, you won't be able to use it again.

Imagine, too, that you are heading for the Arctic. Can you find a testing method for selecting flares that will yield a 3/4 or better probability of ending up with five working flares at your destination? Put another way, can you devise a selection approach that would be expected to provide 75 (or more) out of 100 Arctic visitors with five perfect flares? How would the probability change if the bad pile contained four nonworking flares instead of three?

This article was originally published with the title Five Trusty Flares.

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