# Ask Uncle Colin: These percentages don't add up!

Dear Uncle Colin,

I’m a bit confused! Someone told me that 40% of all Americans on welfare are black, which means that 66% of black Americans are on welfare. How did they work this out?

I don’t get it, and it’s bothering me.

-- Always Back Equality Legistlation

Hi, ABEL! No wonder you’re confused, that 66% figure you’ve been given is way off.

I suspect your initial confusion comes from the problem of different sample spaces: the percentage of Americans receiving welfare who are black isn’t linked (at least not in a trivial way) to the percentage of black Americans receiving welfare.

The source doesn’t give the number of black Americans receiving welfare, but it’s easy enough to work out: it’s 39.8% (the percentage of recipients who are black) of 11,400,000 (the total number of Americans receiving welfare), which is 4,537,200 – given the inexactitude of the figures, I’ll round that to 4.5 million.

According to Wikipedia, there are around 37.7 million people of “non-Hispanic Black or African American” ethnicity in the USA, which makes the percentage of black Americans receiving welfare roughly $\frac{4,500,000}{37,700,000} \times 100 = 11.9%$ – again, accounting for roughness, somewhere around 12%, but certainly nowhere even close to 66%.

-- Uncle Colin

PS: To quote Frank Zappa, I’m not black, but there are a whole lot of times I wish I could say I wasn’t white. This response isn’t about the widespread racial injustice in the USA, it’s not about discrimination, and it’s probably full of clumsy language that could be phrased in a better way. For all of these things, I apologise; my forte is writing about maths. Meanwhile, please follow Wheaton’s Law in the comments. I’m happy to correct errors of phrasing, but I will not tolerate racism or rudeness.