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Counterintuitive Results
Jan. 31st, 2008 01:20 pmA piece on the BBC's website about an infants' school class of 20 pupils in Devon that turned out to be all boys, supposedly by random chance, got me calculating.
Assuming it was totally random, and equal numbers of girls and boys in the population, then the chance of a class of 20 boys or 20 girls would be the same, 1/2^20 or 1 in 1,048,576. But the numbers aren't quite equal, as the population in that age range has 51.2% boys and 48.8% girls. Not a big difference, you might think, but in fact a class of 20 boys is more than twice as likely as a class of 20 girls -- 1 in 647,000 and 1 in 1,719,000 respectively.
Assuming it was totally random, and equal numbers of girls and boys in the population, then the chance of a class of 20 boys or 20 girls would be the same, 1/2^20 or 1 in 1,048,576. But the numbers aren't quite equal, as the population in that age range has 51.2% boys and 48.8% girls. Not a big difference, you might think, but in fact a class of 20 boys is more than twice as likely as a class of 20 girls -- 1 in 647,000 and 1 in 1,719,000 respectively.