Bayesian Scouting

I recently heard some interesting statistics about Scouting. Apparently, even though only one in four boys join Scouting, three out of four of adults holding leadership positions in the business world (representing five percent of jobs) were in Scouting. When I heard this, my first thought was to apply Bayes' theorem. After all, we're given P(S|L), so I was curious to apply Bayes' theorem to find P(L|S), or to use the available information to find what the chances of a Scout ending up a future leader are.

We have that P(S) = 1/4, P(L) = 1/20, P(S|L) = 3/4, and calculate P(L|S) = P(S|L) P(L) / P(S) = 3/20. A similar calculation tells us that P(L| not S) = 1/60, so that it seems that boys who join Scouting are nine times more likely to end up as leaders than boys who don't.

I haven't seen that number before, so I'd guess that the Scouting organization isn't as big a fan of Bayes' theorem as I am.

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