Could having a mental illness make one more likely to be an alcoholic?

They are associated: People with alcoholism are more likely to have certain mental illnesses, particularly anxiety, depression and bipolar disorder, and people with those psychiatric disorders, as well as ptsd and other psychiatric problems, are far more likely to abuse alcohol (and other drugs as well). 1.5% of general population have bipolar disorder, but 15% of alcoholics have it, for example. Ptsd is also common.