Romans 5 says that one man's disobedience made many into sinners. That is essentially the doctrine of original sin in a nutshell directly from the bible.
Rom 5:18-19 KJV Therefore as by the offence of one judgment came upon all men to condemnation; even so by the righteousness of one the free gift came upon all men unto justification of life. (19) For as by one man's disobedience many were made sinners, so by the obedience of one shall many be made righteous.
Because Christ's righteousness is given to us all, then by the same token Adam's sin was given to us all.