Searching for Marilyn Monroe
If in a country 60% are women, 70% have blue eyes, and 80% are blondes, what is the smallest possible percentage of the population who are blue eyed, blonde, women?
Problem source: Activa tus neuronas by laberintos e infinitos.
April 28th, 2009 at 12:39 am
70% of the population has blue eyes. Let’s be wacky and assume that every man has blue eyes. This means that the 30% of the population without blue eyes are all women. It also means that half of all women have blue eyes. The largest possible group of women we can exclude for not having blonde hair is 20% of the overall population. Let’s say that the entire 20% without blonde hair happens to belong to the 30% of the population without blue eyes (who all happen to be women). That leaves just 10% of the population as blonde / blue / women.
Perhaps someone better-versed in statistics could add a bell curve to this and provide the smallest realistically possible percentage as opposed to my smallest theoretically possible percentage.
April 28th, 2009 at 12:44 am
40% are not women, 30% do not have blue eyes, and 20% are not blonde, so at least 100-40-30-20% = 10% are blue-eyed blonde women.
That shows that the answer is /at least/ 10%, but doesn’t show that it /is/ 10% (i.e. that the figure 10% can be attained), so here’s how it can be done:
40% are blue-eyed blond men;
30% are blonde women who do not have blue eyes;
20% are blue-eyed non-blonde women;
10% are blue-eyed blonde women.