Real Life Statistics Problem: I put one jalapeno pepper cut up in chunks in my chili batch. If there are X number of tablespoons of chili in the finished pot, how many pieces of pepper should there be in order to have a 95% probability that there will be at least one pepper piece in each tablespoon? (The total amount of pepper is constant - only the chunk size changes)
The next day I performed two experiments, the first with jalapeno peppers, then red bell peppers, with the same batch of gumbo, figuring it was just as good as chili for my inquiring mind and semi-hungry stomach.
I had no idea how many tablespoons there should be in the batch - didn't care to calculate (I was hungry), so I just guessed at 24 pieces of jalapeno. This was too few as there wound up being 34 tablespoons of gumbo. (Put the gumbo back in the pan.)
Next, I tried 50 pieces of red bell pepper, easily distinguishable from the other ingredients. This time there were fewer tablespoons of gumbo, 30, probably due to some spillage and evaporation of cooking, and thicker soup allowed for a higher piling of contents in the spoon. This time there were 7 spoons out of 30 that had no pieces of red bell pepper; 23% Zero Events.
So 50 pieces of pepper with 30 spoons failed to achieve the original goal of 95% of the spoons having at least one of the desired pepper of the current experiment phase. (Put the gumbo back in the pan again)
When I ate the gumbo I performed one more count. This time there were only 23 tablespoons of gumbo (evaporation, wolves, gremlins, hunger?). There were 4 Zero Events, so I achieved 83% of the spoons having at least one red bell pepper. Sadly though, there was a DAMET (Disappearance Amelia Mary Earhart Type) of 4 out of the 50 pieces of Red Bell Pepper chunks during the ensuing savage soup slurping and sloshing.
Mmmmm...athe..mmmm...atics
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