IntelliJ IDEA “The selected directory is not a valid home for JDK”

Because you are choosing jre dir. and not JDK dir. JDK dir. is for instance (depending on update and whether it’s 64 bit or 32 bit): C:\Program Files (x86)\Java\jdk1.7.0_45
In my case it’s 32 bit JDK 1.7 update 45