As far as I remember, it depends on your OS, browser and JDK version.
Eg. if you are using a 64-bit OS and have installed a 64-bit JDK but are using a 32-bit browser, you may need to install a 32-bit JRE if you need Java support in the browser.
Otherwise, a separate installation of the JRE is not required, since installing the JDK also installs the JRE.
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