{"id":845,"date":"2023-01-19T14:02:40","date_gmt":"2023-01-19T14:02:40","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=845"},"modified":"2023-01-29T18:01:28","modified_gmt":"2023-01-29T18:01:28","slug":"smoking-causes-cancer","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2023\/01\/19\/smoking-causes-cancer\/","title":{"rendered":"Smoking causes cancer"},"content":{"rendered":"\n

Here’s a question posted on Reddit’s statistics forum<\/a>:<\/p>\n\n\n\n

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The Centers for Disease Control and Prevention states on its website that \u201cin the United States, cigarette smoking causes about 90% of lung cancers.\u201d If S is the event \u201csmokes cigarettes\u201d and L is the event \u201chas lung cancer,\u201d then the prob\u0002ability 0.90 is expressed in probability notation as <\/p>\n\n\n\n

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  1. P(S and L). <\/li>\n\n\n\n
  2. P(S | L). <\/li>\n\n\n\n
  3. P(L | S).<\/li>\n<\/ol>\n<\/blockquote>\n\n\n\n

    Let’s consider a scenario that’s not exactly what the question asks about, but will help us understand the relationships among these quantities:<\/p>\n\n\n\n

    Suppose 20% of people smoke, so out of 1000 people, we have 200 smokers and 800 nonsmokers.<\/p>\n\n\n\n

    Suppose 1% of nonsmokers get lung cancer, so out of 800 nonsmokers, there would be 8 cases of lung cancer, 0 caused by smoking.<\/p>\n\n\n\n

    And suppose 20% of smokers get lung cancer, 19% caused by smoking and 1% caused by something else (same as the nonsmokers). Out of 200 smokers, there would be 40 cases of lung cancer, 38 caused by smoking.<\/p>\n\n\n\n

    In this scenario, there are a total of 48 cases of lung cancer, 38 caused by smoking. So smoking caused 38\/48 cancers, which is 79%.<\/p>\n\n\n\n

    P(S and L) is 40 \/ 1000, which is 4%.<\/p>\n\n\n\n

    P(S | L) = 40 \/ 48, which is 83%.<\/p>\n\n\n\n

    P(L | S) = 40 \/ 200, which is 20%.<\/p>\n\n\n\n

    From this scenario we can conclude:<\/p>\n\n\n\n