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Open Facebook in your browser. Click your profile picture. Click the privacy menu on the post you want to change. Click Public.
If prompted, enter your username and password and click Log in. This is on the right of the menu bar or the top of the left sidebar. It will take you to your profile page. This is located just under your name on the post. The icon will match the post's current privacy setting (lock for private, person for friends, or globe for public). The post is now visible to anyone, whether or not they have a Facebook account or are friends with your on Facebook.