Poisson Distribution

For ten tents, p(0) = ten times 0.2231, or 2.231, which is roughly 2. The other 8 tents will probably have at least one fault, and the occupants of those tents are looking at extra KP.

Explanation

We are still using the same sample size (1 tent, or 75 yards of canvas), but we are now taking more samples. The probabilities of occurrence are still what they were, per tent, and we want to know what the distribution might be among 10 tents. For this, it is convenient to reproduce the whole column of the Poisson Table containing the probabilities for r = 1.5. To minimize rounding error, we add together the probabilities for p(4) and all higher numbers, and multiply the given probabilities by 10 to give the expections for 10 tents. The result looks like this:

 r = 1.5 E p(0) 0.2231 2.231 ~ 2 p(1) 0.3347 3.347 ~ 3 p(2) 0.2510 2.510 ~ 3 p(3) 0.1255 1.255 ~ 1 p(4+) 0.0656 0.656 ~ 1 TOT 0.9999 ~ 10

from which it emerges that, in the most likely case, and still assuming random distribution of the manufacturing errors, only 2 tents out of the 10 will be free of defects, and of the 10-man squad, 8 men will be in the kitchen after hours, doing extra KP duty. Unfair, no?

Comment

Maybe. On the other hand, peeling 100 potatoes is not such a hard job when divided among 8 people, and how much worse is that than bayonet drill in the hot sun, which is what the 2 guys with no tent defects are doing right this minute? There is a Chinese story which has the same moral, but if you need Chinese help to see through the paradoxes of seeming good and bad fortune, you are in bad shape.