Translation of "fraction" in a sentence

I'm having difficulty translating the following sentence into Chinese:

A fraction q of the population is smart.

I was tempted to translate this as

But strictly speaking this is not correct, because fraction as a mathematical terminology means 分数 in Chinese (as in a / b for some natural numbers a and b), which is not necessarily a percentage.

Using the literal Chinese translation of fraction doesn't read well:

I'm hoping to get help on a better translation of the sentence. Thank you!

EDIT

From the comments it's clear to me that the English sentence to be translated, taken on its own, may be open to multiple interpretations. I hope the following context will clarify its meaning.

The intended meaning of "A fraction q of the population is smart" is that

The total number of smart people is q * N

given that the population size is N. To put this in full context, the original sentence I am to translate is related to calculating a conditional probability using Bayes' rule:

Suppose p% of the population is educated, and a fraction q of the educated is smart. Suppose further that a fraction r of the uneducated is smart as well. What is the probability that a randomly selected educated person is smart?

Replacing the algebra notations with numbers, the above could have read:

Suppose 73% of the population is educated, and 4/7 of the educated is smart. Suppose further that 2/3 of the uneducated is smart as well. What is the probability that a randomly selected educated person is smart?

• in analogy with 人口的小部分 would 人口的分数q部分 be possible？ Mar 21, 2016 at 19:43
• @user6065: Thanks. Your suggestion definitely sounds better than the literal translation. It got me thinking perhaps "q 部分的人口是聪明的" would be an option as well. Mar 21, 2016 at 19:50
• when feeding "小部分的人口" to jukuu the first 6 results all have 人口的一小部分, if you can say "a/b of the population" then may be you can also leave out 分数 in C Mar 21, 2016 at 20:05
• Let's state it rigorously like a scientific paper. What exactly does "a fraction q of the population" mean in English? (Provided the population is N.) Does it mean "the ratio q / N of human beings is smart", or "the total number of smart people is q * N"? The definition of q is the crux.
– Stan
Mar 22, 2016 at 1:43
• "a fraction q of the population" seems to mean "q of the population" where q would be of the form a/b, a, b positive integers, i.e. if there are N people in the population, it means q*N people as in comment #4 above, with a concrete value for q, as comment #5 says, "fraction" is redundant. In a theoretical discussion with q undetermined, "fraction q" would seem to be correct English. Mar 22, 2016 at 6:04

Suppose 73% of the population is educated, and 4/7 of the educated is smart. Suppose further that 2/3 of the uneducated is smart as well. What is the probability that a randomly selected educated person is smart?

"(Ratio q) + of + X" can be translated as

• (在)X(当)中q. "(在)受过教育的人(当)中4/7是聪明的". And "其中4/7是聪明的" sounds more concise – though IMO it can't be applied to this example because it's a little ambiguous.
• qX. "4/7受过教育的人是聪明的". Sometimes for the subtle fluency, when X doesn't contain "的", it would be better to say "q的X" instead, such as "4/7的农民", "30%的学生".
• X的q. It sounds a little colloquial and a little awkward for this example because there're two close "的"s: "受过教育的人的4/7是聪明的".

(Ratio q) above can be replaced by a percentage "p%" too. Either "(在)受过教育的人(当)中50%是聪明的" or "(在)受过教育的人(当)中p%是聪明的" (p% as a variable) is fine.

However, if you have to use "ratio q" as a variable, it has to be "比例q" or "比率q", and a "有" would be necessary: "受过教育的人中比率q是聪明的". Though maybe not everyone consider it clear enough - "比率q的X" and "X的比率q" patterns are even worse.

PS: I don't see the point of this math problem. If we just randomly select a person within the educated, i.e. P(smart|educated), then, isn't the answer a trivial `4/7`? Have I missed anything? :/

• Sounds like a tricky question, or the "educated" condition in the question is added by mistake. Anyways this answer is spot-on! Mar 22, 2016 at 18:48
• Thanks for the answer. However, my difficulty is not in translating the sentence with numbers in it, but in the sentence with the actual "place-holder" q in it. While 受过教育的人当中4/7是聪明的 sounds fine, 受过教育的人当中 q 是聪明的 sounds awkward. Perhaps 受过教育的人当中有比例 q 是聪明的 would be slightly better? Mar 22, 2016 at 19:44
• Regarding the math, yes, this is a trivial part of a series of non-trivial questions on conditional probabilities. Mar 22, 2016 at 19:51
• @HerrK. You're right and you just replied during my editing that "variable ratio q" part :D
– Stan
Mar 22, 2016 at 19:57
• @Stan Thank you for your help! I appreciate it. Mar 22, 2016 at 20:29

"q比例的人口是属于聪明的。" However this translation is less common in spoken language(Chinese), the more common version we would say is quite like your first translation.

• "百分之 q 的人口" means the ratio = `q%`, but "q比例" (this is not a rigor expression in Chinese either) means the ratio = `q`. Essentially different. To convey the exact meaning of the original author's thought, we need to check the context.
– Stan
Mar 22, 2016 at 5:47
• “q比例的人口是属于聪明的” sounds awkward in Chinese to me. Mar 22, 2016 at 9:05