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"Two independent events", "clickbait": "What do [a pair of dice], [a pair of coins], and [a pair of people on opposite sides of the planet] all have in common?", "textLength": 1029, "alias": "two_independent_events", "externalUrl": "", "sortChildrenBy": "likes", "hasVote": false, "voteType": "", "votesAnonymous": false, "editCreatorId": "16g", "editCreatedAt": "2016-06-16 17:39:52", "pageCreatorId": "16g", "pageCreatedAt": "2016-06-15 08:37:24", "seeDomainId": "0", "editDomainId": "1", "submitToDomainId": "0", "isAutosave": false, "isSnapshot": false, "isLiveEdit": true, "isMinorEdit": false, "indirectTeacher": false, "todoCount": 0, "isEditorComment": false, "isApprovedComment": true, "isResolved": false, "snapshotText": "", "anchorContext": "", "anchorText": "", "anchorOffset": 0, "mergedInto": "", "isDeleted": false, "viewCount": 90, "text": "$$\n\\newcommand{\\bP}{\\mathbb{P}}\n$$\n\n[summary: \n$$\n\\newcommand{\\bP}{\\mathbb{P}}\n$$\nWe say that two [event_probability events], $A$ and $B$, are *independent* when learning that $A$ has occurred does not change your probability that $B$ occurs. That is, $\\bP(B \\mid A) = \\bP(B)$. \nAnother way to state independence is that $\\bP(A,B) = \\bP(A) \\bP(B)$. ]\n\n\n\n\nWe say that two [event_probability events], $A$ and $B$, are *independent* when learning that $A$ has occurred does not change your probability that $B$ occurs. 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