A 1999 article published in the Journal of Developmental Medicine and Child Neurology found a child with Down Syndrome had (at least) a 7% chance of also having an ASD.
As the current prevelence of ASDs in the general population is 1 in 100 (or 1%), a child with Down Syndrome does have an increased risk of receiving an ASD diagnosis.
The study did not have a very large sample size and there is the possibility of compounding factors, so more research in this area is certainly warranted.
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