Which to buy?
You are thinking of buying some new bluetooth headphones on Amazon. You have narrowed your search to three headphones, from four different suppliers. The reviews for each of the headphones are shown below as either thumbs up or thumbs down. Assume that you are only basing your headphones purchase on the reviews and not on other factors (price, technology, small/large business, etc.).
Headphones A: 100% satisfaction (10 thumbs up, 0 thumbs down).
Headphones B: 96% satisfaction (960 thumbs up, 40 thumbs down).
Headphones C: 94% satisfaction (2350 thumbs up, 150 thumbs down).
Headphones D: 97.5% satisfaction (39 thumbs up, 1 thumbs down).
Which headphones should you buy?
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1 solution
No explanation I can give will be as good as 3blue1brown's explanation of the solution to this problem.
Applying Laplace's law of succession (which can be interpreted as saying, "How would the reviews change if there was one extra positive review and one extra negative review?") to the four suppliers yields the following percentages:
A : 1 2 1 1 = 9 1 . 6 7 % , B : 1 0 0 2 9 6 1 = 9 5 . 9 1 % , C : 2 5 0 2 2 3 5 1 = 9 3 . 9 6 % , D : 4 2 4 0 = 9 5 . 2 3 %
Comparing the new reviews of each product shows that headphones B is the preferable product, although headphones D is a close second.