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I know the odds of a human to be an albino. In Europe and the US it is 1 in 20,000 people (source) and for Down syndrome it is 1 in 1,250 (source). So that means the chance of giving birth to a child that has both albino and Down syndrome is:

$20,000 \times 1,250 = 25,000,000$

i.e., 1 in 25,000,000 correct?

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Probability of independent events

Assuming the albinism and Down syndrome are independent traits, then the probability of having both traits is the product of the probability of having each trait.

For more information see wiki > probability (especially the section on independent events).

Albinism and Down Syndrome

If (and only if) albinism and Down syndrome are independent events (see below), then the probability fo having Down Syndrome is $\frac{1}{20,000}$ and the probability of having albinism is $\frac{1}{1,250}$, therefore the probability of having both is $\frac{1}{20,000} \frac{1}{1,250} = \frac{1}{20,000 \cdot 1,250} = \frac{1}{2.5\cdot 10^{7}} = 2.5\cdot 10^{-7}$.

So, yes you were correct! Good job!

Validity of the assumption of independence

I want to highlight again the importance of the assumption that albinism and Down syndrome are independent traits. If a person with Down Syndrome has a different probability of being albino then a person that does not have Down Syndrome, then the probability of having both traits will NOT be the product of the probability of having each trait. The only way to know whether these traits are independent is to look at empirical data. I failed to find any evidence of such correlation (but I might have missed it). If this is a homework question, you should be fine just stating Assuming the two traits are independent,... at the beginning of your answer.

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  • $\begingroup$ Thank you very much for your great answer. Do you know if there was ever a human that was born this way? $\endgroup$ – Florian Neiss Sep 19 '16 at 8:15
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It is correct if (and only if) albinism and Down syndrome are independent events, that is, if albino people is not more nor less likely to have Down syndrome than non albino people (and vice-versa).

However, doing a quick Google search I can't find any source relating albinism and Down syndrome, and therefore independence seems a reasonable assumption unless more information arises and your numbers are right - at least, as right as the sources you are based in.

But beware that your sources are not very representative of what you want to get, or at least not very consistent:

  • Your source for albinism (and its reference) gives prevalence, that is, number of albino people in the whole population of living people in Europe and USA. Please notice that proportion in living population may differ from proportion of births since albino people may have a different life expectancy.
  • Your source for Down syndrome gives a "baseline probability" for a given mother age (young) in some unspecified country. For older ages, probability becames larger.

Then, "the chance of giving birth to a child that has both albino and down syndrome" may differ from that you calculated, specially if you want to use it in circumstances that differ from those your data came from.

Anyway, if you just want a rough estimate, you can use your numbers.

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  • $\begingroup$ This answer is fascianting. Thank you very much. Do you know any case where a human was born this way? $\endgroup$ – Florian Neiss Sep 19 '16 at 8:15
  • $\begingroup$ I'm sorry but I'm not expert in albinism nor Down syndrome - my answer is mostly from statistics. Anyway, according to your numbers we could expect just a few hundred people in the Earth with both, so it's not very likely such cases having been reported. $\endgroup$ – Pere Sep 19 '16 at 8:26
  • $\begingroup$ do you think there are around 100 people or 0 on earth? $\endgroup$ – Florian Neiss Sep 19 '16 at 9:26
  • $\begingroup$ Using your rough approximation, 1 out of 25,000,000 means 280 out of 7,000,000,000. Therefore, if albinism and Down syndrome are actually independent and your sources are representative enough, we could expect a few hundred people on Earth with both. 100 seems more likely than 0. $\endgroup$ – Pere Sep 19 '16 at 9:48

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