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Because Silverlight is still a pretty new internet plug-in, it is known to have a couple of bugs here and there. Like any software, when a new release is updated, many of these bugs are squashed. This could immediately fix any problems that you may have if Silverlight won't install.
If you have Silverlight installed on your computer, you need to remove it before installing a new version; just to make sure that no installation errors occur. To do so, navigate the path Start > Control Panel. From the Control Panel, click the Programs and Features icon to view a list of all installed programs. Find the listing for Microsoft Silverlight from the list and click once to highlight it. Click the Uninstall button. Proceed through the uninstall prompts to complete the uninstall. When you are done, restart your computer.
After your computer starts back up, jump to this page and download the latest version of Silverlight. Open up the installer and install Silverlight onto your computer. After the installer finishes, restart your computer.